BLISS POINT

LSM1301 GENERAL BIOLOGY

2011-12-29T18:02:00.000+08:00

Why did I take this module?

I have taken this module to fulfil my Faculty Requirement for my course. There are only MCQs for the final examinations and there are no mid-term test. However, you have to submit laboratory reports one week after the weekly laboratory sessions.

What have I learned/done?
For this module, you will get to have a better understanding on cells, biochemistry and DNA. Essentially, you will learn everything that is taught for A-level H2 biology. I have participated in 7 laboratory sessions. They are fun and not challenging if you have taken practical exams for your O-levels or equivalent.

Strategies to score well in this module:
1) Buy one of the few recommended textbooks to read. The lecture notes are NOT sufficient for you to do well.

2) The final examination questions can be tricky. If you think the answer to a question is damn obvious, think again - it can be another trick question. =)

3) Although it's an open-book examination, avoid searching through the textbook/notes for all the questions. You do not have the luxury of time. If time is running out, just shade C (A, B or D is also fine) for all the rest of the questions. The rationale is not to leave any question blank!

4) Use colour tags so as to increase your efficiency in looking for answers in the textbook. Don't underestimate the usefulness of the index section of the textbook. You may choose to make a copy of the index section before the final examination for easy referencing.

5) Put in effort for your laboratory report. Avoid any mistakes! Most people will score high grades for this lab component. Try to get reports from seniors to get an idea what is expected of you.

Risk Taking - Odds (Part I)

2011-12-29T11:36:00.000+08:00

DISCLAIMER: I AM NOT PROMOTING GAMBLING! BUT IF YOU REALLY CHOOSE TO GAMBLE, DO IT RESPONSIBLY!

In this article, I seek to provide an intuitive understanding to the idea of odds.

I will be using the decimal odds system in this article. This is the odds system used by Singapore Pools (the only legal bookmaker in Singapore). ‘Decimal odds, also known as European odds, express the amount of money which will be returned to the punter on a 1 unit stake. For example, if Barcelona is favoured to win at 1.50, then a $100 bet will give you back $150 in total. ’ <http://www.online-betting.me.uk/articles/how-to-read-betting-odds.html> If Barcelona really wins the match, the punter will get back your $100 capital and enjoy a winning of $50. However, if Barcelona loses the match, the punter will lose the $100 capital.

1) How does the bookmaker come out with odds?

I am not sure. Most probably, the bookmaker uses some form of complicated statistical model.

2) What information can punter obtain from the odds provided by the bookmaker?

We can know about bookmaker’s view for that game. If the odds are lower as compared to other options (such North Korea winning that match), it means that the bookmaker thinks that Barcelona has a high chance of winning the match. However if Barcelona's odds are higher as compared to other options, it means that the bookmaker thinks that Barcelona has a lower chance of winning the match.

3) Should you place a bet for an option with higher or lower odds?

It is really up to you. For an option with higher odds, the chance of occurring is lower but the reward is higher. For an option with lower odds, the chance of occurring is higher but the reward is higher. It is risk-reward issue.

In the next article, I shall be using some simple probability ideas to discuss more interesting issues such as, when should you (a rational person) place bet for a game?

SSS1207 NATURAL HERITAGE OF SINGAPORE

2011-12-28T17:40:00.000+08:00

Why do I take this module?

I took up SSS1207 to fulfil my University Requirement for my course. Out of all the available Singapore Studies modules, this is the only one which does not require me to memorise anything or to answer open-ended questions in the mid-term test or the final examination.

What have I learned/done?

I have a better understanding of the Singapore’s existing biodiversity and habitats. As part of the field practical. I went to Sungei Buloh Nature Reserve, Kent Ridge Park, Bukit Timah Naure Reserve and Raffles Museum of Biodiversity Research.

Strategies to score well in this module:

1) Try to go for as many field trips as possible. These field practicals will enhance your learning.

2) Participate actively in the IVLE discussion forum. Try to contribute at least once every week. If you go for the field practicals diligently, you will always have something to say. I will have a separate blog article on this! Stay tuned. =)

3) Lastly, I have uploaded my essay in the post titled "SSS1207 Essay Sample". You may want to take a look to have some idea what could be the type of essays you are expected to come out with if you take this module.

WHAT'S INSIDE A TRANSPONDER?

2011-12-28T01:03:00.000+08:00

In case anyone wonder what's inside a transponder. No transponder was damaged in the process and the transponder opened up by itself. =)

PC2193 Sample Lab Report - BASIC DIODE ELECTRONICS

2011-12-27T14:48:00.000+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

PC3231 (AY10/11 SEM 1) FINAL EXAMINATION SUGGESTED SOLUTION

2011-12-27T01:44:00.000+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ENSURE THE QUALITY OF THE SOLUTION. HOWEVER, THE AUTHOR IS NOT RESPONSIBLE FOR ANY LIABILITIES THAT ARISES DUE TO QUALITY OF THE SOLUTION.

I have volunteered to come out with the suggested solutions for PC3231's final examination questions. Since it's my work, so I decided to share with you all. The examination paper can be obtained from http://libportal.nus.edu.sg/frontend/index.

GEM2900 CA Question

2011-12-27T01:34:00.000+08:00

The following question is modified from the AY 09/10 Semester 1 CA3. I posted this as one of the few common kind of question that you are expected to solve for this module.

A marble is placed in the bag. The marble is equally likely to be black or white and you don't know its colour. Next, another marble is placed in the bag, this time it's a white marble (you do know the colour). The bag is shaken and one of the marbles is drawn at random. It is white. What is the probability that the marble remaining in the bag is also white? Now, we put it back white marble into the bag and perform the another draw. What is the chances that we will see a white marble on the second draw?

I will post the solutions and other CA questions when I am free. =)

Risk Taking - League Table Quiz

2011-12-27T00:06:00.003+08:00

I chanced upon this question while I was browsing through books on psychometric test. It was mentioned in the book that this is the hardest question that can possibly appear in the numerical reasoning test. However, I strongly believe that any punters that place bets for soccer games should be able to solve this question.

Suppose there are 6 soccer teams: Team Alpha, Team Beta, Team Delta, Team Gamma, Team Omega and Team Sigma. As usual, a team will receive 3 points if it wins a match but will not receive any point if it loses that match. However, if the game ends in draw, both teams will each receive 1 point for that game. Let us also assume that each team will play with the remaining 5 teams once for the whole season. The following is the league table for that 6 soccer teams:

No of matches played Total Points
Team Alpha 4 10
Team Beta 4 9
Team Delta 4 6
Team Gamma 4 6
Team Omega 4 1
Team Sigma 4 0

Q1) So far, how many matches have taken place?

Q2) Which of the above-mentioned team(s) can still be the champion for this season?

Q3) Which of the above-mentioned team(s) can still finish last for this season?

I will supply the answers in another post =D

DIMENSIONAL CONSISTENCY?!

2011-12-26T11:58:00.002+08:00

Just for fun! A 'good' example which shows that dimensionally consistency does not imply that the equation is valid.

TACOMA NARROWS FALLACY

2011-12-26T11:29:00.001+08:00

Tacoma Narrow did not collapse due to resonance driven by the wind! It's actually due to AEROELASTIC FLUTTER. I was 'tricked' by the the textbooks too. =(

WORDS OF THE DAY (26 Dec 2011)

2011-12-26T02:16:00.003+08:00

INEXORABLE

Definition(s) of INEXORABLE

1. Not to be stopped.

Example(s) of INEXORABLE

1. The price of gold has risen inexorably year-after-year.

INTREPID

Definition(s) of INTREPID

1. Brave; daring; fearless.

Example(s) of INTREPID

1. The intrepid boy wants to climb Mount Everest on his own when he grow up.

WHY DO I WANT TO PARTICIPATE IN SEP?

2011-12-24T00:20:00.001+08:00

For undergraduates in the Faculty of Science, you would need craft a personal statement that highlights your contributions to NUS, school etc, as part of the Student Exchange Programme (SEP) process. In addition of that, you would also need to justify why you really want to participate in SEP. You may have the urge to say "I just want to have fun" or "I just want to freeze my ever-falling CAP". However, these are not 'good' reasons which will get you selected for SEP. Here, I would like to share on why I want to participate in SEP:

I would like to take part in the NUS Student Exchange Programme (SEP). Thereare 3 reasons for joining SEP.

Interms of academic studies, there will be greater freedom in choosing whatcourses to study, thus enabling me to explore new areas of study and interest.Going for SEP allows me to take interesting physics modules which are currentlyunavailable in NUS, such as Current Interpretations ofQuantum Mechanics (University Of Toronto. In addition, the teachingstyles in foreign universities will be different from Singapore. It will be achallenging and yet exciting experience to learn and think from otherperspectives.

Tome, SEP will be a journey that is advantageous to character building andpersonal development. Being at a foreign country, I am prepared to step out ofmy comfort zone and handle various situations myself. My problem solving skillswill be honed as there will be many challenges along the way waiting for me toovercome. My decision-making capabilities will also be developed as I have tomake important decisions on my own and live with them. After the SEPexperience, I believe I will become a more confident and independent personwith better decision-making and problem-solving skills.

Goingfor SEP will enrich my cultural experiences. In today’s globalised world, it’sessential that we seek global exposure and get to know more about the differentperspectives of people from other countries, understand how they think, andlearn how to communicate effectively with them despite the slight languagebarrier. This will definitely prepare us to work in a more culturally diversesociety. In addition, I will meet more people from diverse backgrounds and thiswill widen my social circle and definitely also be beneficial for my futurecareer.

Allin all, I believe that going for the Student Exchange Programme is an importantpart of university life which, given a chance, I will definitely want to gofor. There are many opportunities and avenues where I can learn more aboutother cultures and myself through the Student Exchange Program. Such learningopportunities will offer valuable life lessons that I may not ever be able tolearn in the whole of my life.

SEP MODULE MAPPING

2011-12-23T23:57:00.001+08:00

It was often said that module mapping is the hardest component of SEP application. I cannot agree more. Thus, I would like to share with you the 10 modules offered by University of Toronto (UofT) which have been accepted by NUS Science Faculty.

PHY491H1 PHY357H1 PHY452H1 PHY450H PHY354H PHY358H1 MAT2241H1 MAT363H1 PHY454H1 MAT337H1 PC4991 PC3232 PC4241 PC4242 MA4248 PC3235 MA2101 MA3215 PC3238 MA2108

Why is the gravitational potential energy is always negative?

2011-12-23T22:51:00.000+08:00

Recently, I receive a email from a tuition centre which is looking for new tutors. In that email, there is the application form. The title for this post is one of the two essay question that an applicant has to answer before submitting the form. Here, I shall attempt to answer this question. =)

The answer to this question is quite simple - by convention! This is due to our convention of setting the gravitational potential energy as zero at infinity (a very very very far point, at the edge of our universe, if there is one). Consider the usual scenario where a man throws a ball up into the sky. The potential energy of the ball increases as the ball move away from the surface of the Earth. The gravitational potential energy of the ball increases when we move further away from the surface of the Earth. In other words, the gravitational potential energy of the ball decreases when we move nearer to the surface of the Earth. Since the gravitational potential energy for all objects (including the ball in this usual scenario) are zero at infinity and decreases while we consider points that are nearer to the surface of the Earth, we can readily see from a number line (...,-100. -99, -98,....., -3, -2, -1, 0) that the values of the gravitational potential energy for this ball must be negative.

Recall that energy is just a value we assign to an object which describes the dynamical nature of the object. By dynamical nature, I mean the velocities of the objects and relative positions between the objects. The value we assign does not really matter! The change in energy before and after a interaction is the only important thing. This is why we can just set the infinity as the point with zero gravitational potential energy without much worry.

You may be wondering why we need to take the above convention and generate that nasty negative signs all over the place. Consider the Moon that is revolving around the Earth. We assume that there are no other planets or stars that are having significant gravitational influence on the Moon. The negative sign for gravitational potential energy has also caused the total energy of a Moon to acquire a negative sign. This negative sign indicates that the Earth-Moon is a bound system. The Moon will not move away from the Earth on one fine day without any external disturbance. In order for the Moon and the Earth to move away from each other, we need to supply some energy to this two-body system. For example, we can attach many nuclear-powered rockets on the sides of the Moon and you will most probably see our Moon really drifting away from us. In summary, the additional benefit for having a negative gravitational potential energy is that we can create another useful convention. That is, if total energy for a two particle system is negative, we can conclude that the two particles are bounded to one another (just like a couple that is deeply in love).

You see this 'problem' of having negative total energy in electrostatic problems too, in particular, a hydrogen atom. Observe that the energies of the hydrogen energy levels are always negative values. For example, if the hydrogen atom is in the ground state, the total energy of the system is -13.6eV. From this, we can conclude that the electron is tightly bounded to the proton (nucleus of he hydrogen atom) if the atom is in the ground state.

ANGRY BIRDS AND PHYSICS EDUCATION

2011-12-23T11:50:00.000+08:00

Since Angry Bird is such a popular game, it is not surprising that it become a Physics examination question.

More interesting ideas on how the Angry Bird game is utilised in the classroom can be found on John Burk's (ninth-grade physics teacher at the private Westminster Schools) blog: http://fnoschese.wordpress.com/2011/06/16/angry-birds-in-the-physics-classroom/

PC2193 Sample Lab Report - X-RAY DIFFRACTION OF CRYSTALS

2011-12-21T13:34:00.000+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

PC3193 Viva Questions - DUANE-HUNT AND PLANCK’S CONSTANT

2011-12-20T00:05:00.002+08:00

The following are the questions that were posed to me during my oral examination on Duane-Hunt and Planck’s Constant:

1) What is the Duane relation?

2) How is x-ray being produced? Cathode, anode, andthe wiring.

3) How the graph obtained? (Using a goniometer.Making use of the NaCl crystal.)

4) Draw the diffractogram.

5) What is the difference between the whaleback and characteristic X-ray lines

6) How are the characteristic x-ray lines formed?

7) What does the NaCl act as? (Diffraction grating.)

8) What is the underlying principle behind this experiment? (Bragg law.)

9) How do you get the best fit line with thegreatest gradient?

10) What is your Planck's constant error? (Compare error withuncertainty. The uncertainty should be as large as the percentage discrepancy.)

PC3193 Viva Questions - NUCLEAR MAGNETIC RESONANCE

2011-12-19T23:57:00.002+08:00

The following are the questions that were posed to me during my oral examination on Nuclear Magnetic Resonance:

1) What is nuclear magnetic resonance? (Spin, ZeemanEffect and driving field = energy gap.)

2) How much information can you obtain from thesignal? (Position, frequency, amplitude and FWHM)

3) What affects the position?

4) What affects the FWHM? (Chemical environment.)

5) What affects the amplitude? (The density ofstates of the higher energy level.)

6) How many of the 6 samples have protons as thedominating source? (5. Judging from the frequency. Almost the same for the 5 of them)

7) How do you get the graph and the uncertainty ofthe g-factor?

8) Did you compare the g-factor with the literaturevalues?

9) How does a teslameter works.

PC3193 Viva Questions - KERR EFFECT

2011-12-19T23:52:00.002+08:00

The following are the questions that were posed to me during my oral examination on Kerr Effect:

1) Why did you not take readings near the maximumand minimum points so as to ascertain accurately the U_max and U_min?

2) Why do you take readings until you get U_min?

3) Explain what does it mean by linearly,circularly and elliptically polarised?

4) How do you get the equation (with the sinesquared)?

5) What is the laser used and how is laser lightformed?

6) How do you improve on the experiment?

PC3193 Sample Lab Report - KERR EFFECT

2011-12-19T15:26:00.002+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC3193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

PC2193 - Oral Presentation for Magnetic Moments in Magnetic Field

2011-12-19T14:58:00.001+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS PRESENTATION SLIDES IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD PRESENTATION.

For the oral presentation for PC2193, you are allocated 10 minutes to talk about any experiments that you have performed. You might be wondering why I am presenting on this topic - The background information for this experiment is ridiculously simple! This means that you can have more time to present your findings and impress the professors on your data-analysis.

At the end of your presentation, the professors will take turn to ask you question regarding your presentation. Hence, ensure that you understand every sentence or diagram you have included in your slides. For me, Prof. Tang asked me: "If the circular is not small, what will be the effect(s)?" I shall leave you to think about this question yourself. =)

PC2193 Sample Lab Report - BAND GAP OF GERMANIUM

2011-12-19T14:38:00.000+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

PC2193 Sample Lab Report - LAW OF DISTANCE AND ABSORPTION OF GAMMA RAY

2011-12-19T14:33:00.001+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

Work done can be negative, however it is a scalar?

2011-12-19T13:57:00.000+08:00

PC2193 Sample Lab Report - ELECTRON SPIN RESONANCE

2011-12-19T13:24:00.003+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR PC2193 STUDENTS. IT IS BY NO MEAN A BENCHMARK FOR A GOOD LABORATORY REPORT.

PC2193 Sample Lab Report - MAGNETIC MOMENT IN MAGNETIC FIELD

2011-12-19T13:03:00.002+08:00

MagneticMoments in the Magnetic Field

Aconductor loop carrying a current in a uniform magnetic field experiences atorque. In this experiment, investigations were carried to determine how torqueexperienced by the conductor circular coil depends on the strength of themagnetic field (Part I), the angle between the magnetic field (Part II) and thestrength of the magnetic moment of a circular conductor coil (Part III, IV andV). The experimental results obtained have providedstrong evidence that the torque varies linearly with the strength of themagnetic field, the angle between the magnetic field and the strength of themagnetic moment.

I.INTRODUCTION

Aconductor loop carrying a current in a uniform magnetic field experiences atorque. The aim of this experiment is to investigate how the torque experiencedby the circular conductor coil depends on the strength of the magnetic field,the angle between the magnetic field and the magnetic moment, the square of thediameter of the circular coil (area), the number of turns of the coil and thecurrent flowing through the coil.

II.THEORY

Consider a planar current loop C with currentI. The dipole moment of the wire loopis given by

. (1)

The vector is perpendicular to the plane of the loop (Fig.1) and its magnitude is equal to the infinitesimal area element of the loop.

Figure 1 A planar current loop withcurrent I. The origin 0 is arbitrary.The shaded region shows the infinitesimal areaelement of the loop.

Thus,

, (2)

where is the normal vector, and A is the area of the loop. The dipole moment vector pointsperpendicular to the loop and its magnitude depends on its area, number ofturns and the current in the coil. The shape of the loop is irrelevant as longas the current loop is planar.

The torque on the planar loop, due to themagnetic force on the current distribution, is given by

(3)

provided that themagnetic field is a uniform.. Equation(3) tells us that the torque due to a uniform magnetic field is a function ofstrength of the magnetic field, angle between the magnetic field strengthvector and magnetic moment vector, and strength of the magnetic moment.

III.THE EXPERIMENT

Figure 2 Helmholtz coils. Distance betweenthe two coil d = radius of the coil. The mid-plane lies in between and parallelto the two coils and the central axis passes through the centre of the twocoils. The dotted lines show the pattern and direction of the magnetic fieldlines

A homogenous magnetic field required for thisexperiment was achieved by making use of the Helmholtz coils (Fig. 2). Helmholtzcoils consist of two circular magnetic coils that are placed symmetrically oneon each side of the experimental area along a central axis. The Helmholtz coilsused in this experiment has a diameter of 400mm and 154 turns. When the separationbetween the two circular Helmholtz magnetic coils is equal to the radius of thecoil itself, the non-uniformity of the magnetic field along the central axis willbe minimised. The magnetic field generated is proportional to the current I’ in the Helmholtz coil (Biot-Savartlaw). The two Helmholtz coils were connected in series to ensure that the magnitudeof current flowing in them was the same. The current through the coils was keptbelow 3A to allow continuous operations. The wires connecting the power sourceto the coil carrier were twisted so as to prevent additional magnetic momentproduction.

A circular conductor loop of diameter d and n number of turns was suspended from the torsion balance, with the central axis (refer to Fig. 2) cuttingthrough the centre of the conductor coil. The area of the coil is . The torque onthe circular conducting coil was measured by thetorsion dynamometer. The torsion dynamometer only provides measurements inunits of force. As the length of the moment arm (torsion bar) remains unchangedthroughout the whole experiment, hence for convenience the readings obtainedfrom the torsion dynamometer will be treated as torque in this report (and herebybe called as ‘torque’). As the magnitude of the torque produced was very small,conductor loop with the most number of turns (3 turns) and maximum allowableconductor loop current (about 5A) were used whenever possible in order to obtainlarger torque measurements. It will help to reduce the percentage uncertaintyof the measurements. The large current also helped to make the effect of theEarth’s magnetic field less comparable to the magnetic field generated by theHelmholtz coils.

Figure 3 Experimental setup. The labels A,B, C and D indicate the DC source for the Helmholtz coil, multimeter to measurethe current in Helmholtz coil I’, DCsource for the conductor loop and multimeter to measure the loop’s current I, respectively. The labels E, F, and G referto the torsion dynamometer, Helmholtz coil and the conductor loop,respectively.

At the start of each experiment, the zero-point of the torsion balance was ensured. It was alsochecked frequently, since rapid rotary movements of the coil can displace theconnecting leads. ‘Torque’ measurements were only taken after the circular coilstopped moving (in equilibrium).

There were five parts to the experiment (PartI to V) and each of them were designed to find out how the torque experiencedby the conductor circular coil depends on a particular physical variables (Table1) while all other physical variables were kept constant. Multiple readingswere taken for each part of the experiment and the average values were found soas to reduce the effects of random errors.

PART	PHYSICAL VARIABLES
I	Helmholtz coil current I’
II	Angle θ.
III	Area of coil A
IV	Number of turns n
V	Coil current I

Table 1 Different parts of the experimentand the physical variables examined.

In Part I, the Helmholtz coilcurrent I’ was varied by adjustingthe power knob of the DC source (Fig. 3, label A) until the desirable value wasreflected on the multimeter (Fig. 3, label B). For Part II, the angles should be set at 15° intervals by alternate use ofthe notches in the coil carrier. In Part III, coils of different diameters d wereused. For Part IV, coils with different number of turns (n) were used. In PartV, the coil current I wasvaried by adjusting the power knob of the DC source (Fig. 3, label C) until thedesirable value was reflected on the multimeter (Fig. 3, label D).

According to the discussion on magnetic moment and torque in the theorysection, the magnitude of the torque should have the following relationship:

(4)

where c is a constant. Table 2shows the list of independent variables in which a straight line that passesthrough the origin should be obtained when a graph of torque against any of theindependent variable is plotted.

PART	Independent Variable
I	I’
II	sinθ
III	d²
IV	n
V	I

Table 2 Torque has linear relationshipwith the abovementioned independent variables and each of these relationshipswere studied in one the 5 parts of this experiment.

IV.RESULTS

A. PART I

Fig. 4 presents the graph of ‘torque’ againstHelmholtz coil current I’. The bestfit straight line was drawn using linest() function of Microsoft Excel. Theerror bars on the data points are calculated based the uncertainty in the‘torque’ measurement using the torsion dynamometer. The linear correlationcoefficient of the best fit line is found to be 0.9975.

Figure 4 Graph of ‘Torque’ againstHelmholtz coil current I’.

B. PART II

Fig. 5 presents the graph of ‘torque’ againstsinθ. Positive sinθ values were assigned when the circularcoil turned counter-clockwise when viewed from the top of the torsiondynamometer while negative sinθvalues were assigned when the coil turned in the opposite direction. The bestfit straight line was drawn using linest() function of Microsoft Excel. Theerror bars on the data points are calculated based the uncertainty in the‘torque’ measurement using the torsion dynamometer. The linear correlationcoefficient of the best fit line is found to be 0.9980.

Figure 5 Graph of ‘Torque’ against sinθ.

C. PART III

Fig. 7 presents the graph of ‘torque’ againstd². This graph Only 3 datapoints can be obtained as there were only 3 coils with different diameter. Thebest fit straight line was drawn using linest() function of Microsoft Excel.The error bars on the data points are calculated based the uncertainty in the‘torque’ measurement using the torsion dynamometer. The linear correlationcoefficient of the best fit line is found to be 0.9999.

Figure 6 Graph of ‘Torque’ against d².

D. PART IV

Fig. 7 presents the graph of ‘torque’ againstnumber of turns n. Only 3 data pointscan be obtained as there are only 3 coils with different number of turns of coils.The error bars on the data points are calculated based the uncertainty in the‘torque’ measurement using the torsion dynamometer. The error bars are toosmall and hence they are not included in the graph. The linear correlationcoefficient of the best fit line is found to be 0.9985.

Figure 7 Graph of ‘Torque’ against numberof turns n.

E. PART V

Fig. 8 presents the graph of ‘torque’ againstcurrent in circular coil I. The bestfit straight line was drawn using linest() function of Microsoft Excel. Theerror bars on the data points are calculated based the uncertainty in the‘torque’ measurement using the torsion dynamometer. The linear correlationcoefficient of the best fit line is found to be 0.9875.

Figure 8 Graph of ‘Torque’ against currentin circular coil I.

V.DISCUSSION

The correlation coefficient rof the data in Part I (5 data points) has a value of 0.9975. According tostatistical theory, there is only 0.05% probability of obtaining r= 0.974 for 5 data points ifthe data are not correlated. Hence, the correlation coefficient r for the data, shown on Fig. 4, providesconvincing evidence that ‘torque’ is directly proportional to I’.

The correlation coefficient r ofthe data in Part II (13 data points) has a value of 0.9985.According to statistical theory, there is only 0.05% probability of obtaining r= 0.801 for 13 data pointsif the data are not correlated. Hence, the correlation coefficient r for the data, shown on Fig. 5,provides convincing evidence that ‘torque’ is directly proportional to sinθ.

The correlation coefficient r ofthe data in Part V (8 data points) has a value of 0.9875.According to statistical theory, there is only 0.05% probability of obtaining r= 0.925 for 8 data points ifthe data are not correlated. Hence, the correlation coefficient r for the data, shown on Fig. 8,provides convincing evidence that ‘torque’ is directly proportional to I.

No concrete statisticalconclusion can be made regarding the relationship between‘torque’ and d², and between ‘torque’ andthe number of turns n. This is due tothe small number of data points (only 3) gathered in these two parts of theexperiment. As mentioned earlier, the lack of data points is due to thelimitation in the experimental apparatus available to the author for these twoparts of the experiment. One obvious possible improvement for this experiment isto use more coils with different diameter and number of turns so as to providemore convincing evidence of the linear relationship. However, judging from thehigh correlation coefficient values (0.9999 for ‘torque’ against d²_;0.9985 for ‘torque’against number of turns n) obtained fromthe data points, there is a high chance that that ‘torque’ has a linear dependenceon area (d²) and number ofturns of coil n.

According to equation (4), the y-interceptfor all the 5 graphs (Fig. 4 to Fig.8) should cut through the origin. Part 1shows substantial deviation from the theoretical results as the value of the y-intercepthas almost the order of magnitude as the smallest division of the ‘torque’measurements. The best-fit lines on Part II to IV also fail to cut the origin. Allthese could be due to systematic errors. The possible misalignment of theretort stand has led to the torsion bar having an initial angle with the Helmholtzcoils. In addition, the author was unable to ensure that the coil is parallelto the Helmholtz coil during the initial alignment before the start of eachpart of the experiment.

The apparatus used were inconveniently placedon the laboratory table. As a result, the torsion dynamometer was much aboveeye-level. The author had to climb onto a stool to read off the values on thetorsion dynamometer and to check the alignment of torsion bar to the balancepoint. Consequently, parallax error may be introduced due to the uncomfortablenature of the actions. The climbing onto the stool also caused the torsionbalance to sway and disturbed the overall setup of the equipment. All theseerrors can be avoided by positioning all the apparatus on the floor.

The torsion dynamometer has poor level ofprecision as the smallest division is 0.1mN. There were many instances that thepointer fell within the unmarked spaces on the scale. This has contributed tothe uncertainty in the experiment.

Other than Part III, there was no choice inthe size of the coils used in other parts of the experiment. Smaller coilsshould be used in other parts of the experiment so that the magnetic fieldinside the circular coil would be more uniform.

VI.CONCLUSION

The aim of thisexperiment is to investigate how the torque experienced by the conductorcircular coil depends on the strength of the magnetic field, the angle betweenthe magnetic field and the magnetic moment, the area of the circular coil, thenumber of turns of the coil and the current flowing through the coil. Thesewere achieved by measuring the torque experienced by the current carryingcircular coil under the influence of the magnetic field generated by the Helmholtzcoil using a torsion dynamometer. The experimental results obtained have providedstrong evidence to show that the torque have linear dependence on strength of the magnetic field, angle between themagnetic field and magnetic moment, and strength of the magnetic moment of thecircular coil.

VII.REFERENCES

1. Laboratory Manual for PC2193 Magnetic Moments in theMagnetic Field.

2. Griffiths,David J, Introduction toElectrodynamics, 3rd ed. (Addison Wesley, 1999), p.242-246.

3. Gerald Pollack and Daniel Stump,Electromagnetism,1st ed. (Addison Wesley, 2002),p.284-291.

PC2230 THERMODYNAMICS AND STATISTICAL MECHANICS

2011-12-18T18:13:00.009+08:00

Why did I take this module?
This is one of the 5 compulsory level 2 physics modules that a physics major has to take.

What have I learned?
This module is an introductory course in statistical and thermal physics, and is a prerequisite to advanced statistical mechanics. The topics to be covered include: mathematical background, laws of thermodynamics, thermodynamics functions, chemical equilibrium and phase transitions, kinetic theory, postulates of statistical mechanics, independent particle approach of statistical mechanics, basic distributions, ideal gases, paramagnetism, equipartition theorem, etc. Science and engineering students with a background knowledge of general physics are the targeted students. (Extracted From NUS Bulletin)
Personally, I am amazed that I have a better understanding of equilibrium constants, a concept that learned in my A-level chemistry class.

Strategies to score well in this module:
1) Have a COMPREHENSIVE cheat sheet! Squeeze ALL the essential derivations that appear on the lecture notes, unless you have a good memory. There are always questions which require you to reproduce those derivations. Don't be lazy, or else Murphy's law will make you regret.

2) The 138 pages of lecture notes prepared by Prof. Ng is more than sufficient. Thus, you may choose not to read the textbook. Just be attentive in class and avoid skipping any lectures.

CAD/SGD Forex Charts (Last 30 days)

2011-12-18T02:00:00.000+08:00

Last 30 days trading for CAD/SGD

CAD/SGD Forex Charts (Last 7 days)

2011-12-18T01:59:00.000+08:00

Last seven days trading for CAD/SGD

CAD/SGD Forex Charts (Last 24 hours)

2011-12-18T01:57:00.000+08:00

Last 24 hours trading for CAD/SGD

PC3193 Viva Questions - FTIR

2011-12-17T23:25:00.000+08:00

The following are the questions that were posed to me during my oral examination on FTIR:

1) What is FTIR?

2) Explain how does the Michelson Interferometer works?

3) How is the transmission spectrum obtained?

4) What is the relationship between power spectrum, transmission spectrum and background spectrum?

5) What compounds are responsible for the peaks in the background spectrum? (carbon dioxide, water vapour)

6) What is a evanescent wave?

7) Explain how does the ATR works?

8) What is spectral subtraction?

9) How do you determine the appropriate factor for spectral subtraction?

USD/SGD Forex Charts (Last 30 days)

2011-12-16T22:28:00.000+08:00

Last 30 days trading for USD/SGD

USD/SGD Forex Charts (Last 7 days)

2011-12-16T22:27:00.000+08:00

Last seven days trading for USD/SGD

USD/SGD Forex Charts (Last 24 hours)

2011-12-16T22:26:00.000+08:00

Last 24 hours trading for USD/SGD

CHANGING EDUCATION PARADIGMS

2011-12-16T12:13:00.000+08:00

MASS, WEIGHT AND DENSITY

2011-12-15T12:22:00.000+08:00

Mass

Mass is the measure of the amount of substance in a body.
Unit of mass: kilogram (kg), gram (g)
Scalar quantity
Measured using a beam balance
Fixed value
Inertia is directly proportional to mass. Inertia is the object’s reluctance to start/stop moving.

Volume

Volume is amount of space the object occupies.
The volume of the solid/liquid can be obtained using a measuring cylinder
The volume of a regularly shaped solid or an irregularly shaped solid which sinks in water can be determined using displacement method.

Gravitational field

Gravitational field is a region in which a mass experiences a force due to gravitational attraction.
The strength of the gravitational field is due to the mass of the planet
Gravitational field strength, g, measures the strength of the gravitational field
Unit of gravitational field strength: Nkg-1
g = 10 Nkg-1 at the surface of the Earth
The strength of the gravitational field decreases as we get further away from the planet

Weight

Weight is the gravitational force on the body.
Units: Newton (N)
Vector quantity. Points downward.
Measured using a spring balance
Weight = mass × gravitational field strength
Weight depends on the distance of the object from the planet

Density

Density is mass per unit volume
Units of density: kgm-3, gcm-3 (1000kgm-3 = 1gcm-3)
density = mass/volume.
Scalar quantity
Depends on type of material. Objects of different sizes made up of the same material will have the same density.
The density of object can be obtained by measuring both the mass (beam balance) and volume of the object (displacement method). Then, use the equation (density = mass/volume)
Average density = total mass/total volume
Generally, heating causes an increase in volume without an increase in the mass. Density decreases. (Convection)
If the object has a higher density than the surrounding medium, the object will sink. If the object has a lower density than the surrounding medium, the object will float. If the object has the same density as the surrounding medium, the object will suspend in the medium

PHYSICS OF THE RIDERLESS BIKE

2011-12-13T11:17:00.000+08:00

It looks like magic. A bike traveling at the right speed will steer itself--popping back up when it starts to fall. But why? A new paper by Andy Ruina, of Cornell University, Jim Papadopoulos, of University of Wisconsin - Stout, and colleagues challenges the conventional wisdom of what's required for bike stability.

CORONA DISCHARGE

2011-12-13T01:09:00.000+08:00

This video was captured by me when I was using the X-ray Diffraction machine. Normally, this will not occur if you have warmed up the X-ray machine before the start of the experiment. =P

SCHRÖDINGER'S CAT

2011-12-12T11:34:00.000+08:00

A good video that introduces the idea of superposition of states and effects of measurements in a light-hearted way.

Another good video on Schrödinger's Cat. Curiosity may really kills the cat! =P

DOUBLE SLIT EXPERIMENT

2011-12-11T12:16:00.000+08:00

Electron interfering with itself?! A mind-blowing video that leave me puzzled everytime I watch it, even though I have completed my undergraduate quantum physics courses.

IS HELL EXOTHERMIC (GIVES OFF HEAT) OR ENDOTHERMIC (ABSORBS HEAT)?

2011-12-09T11:54:00.000+08:00

The following is an actual question given on a University of Washington engineering mid-term.

The answer was so "profound" that the Professor shared it with colleagues, and the sharing obviously hasn't ceased...

Bonus Question:
Is Hell exothermic (gives off heat) or Endothermic (absorbs heat)?

Most of the students wrote
Proofs of their beliefs using Boyle's Law, (gas cools off when it expands and heats when it is compressed) or some variant.

One student, however, wrote the following:

"First, we need to know how the mass of Hell is changing in time.
So we need to know the rate that souls are moving into Hell and the rate they are leaving.
I think that we can safely assume that once a soul gets to Hell, it will not leave.
Therefore, no souls are leaving. As for how many souls are entering Hell,
let us look at the different religions that exist in the world today.
Some of these religions state that if you are not a member of their religion, you will go to Hell.
Since there are more than one of these religions and since people do not belong to more than one religion,
we can project that all souls go to Hell.
With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially.

Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand as souls are added.
This gives two possibilities:
1. If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose.
2. Of course, if Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over.

So which is it?
I am sure that Hell is exothermic and will not freeze."

This student received the only A..

My Module Selection

2011-07-27T21:19:00.007+08:00

I have taken the following modules in NUS. I have chosen the modules strategically so as to maximize my welfare. However, I do have some form of regrets and these can be a good learning lesson for you too.

I have planned my modules before the start of my university life. I took into account for all aspects of my major (Physics) requirement. I have dugged out all the potential modules using NUS Bulletin and CORS. In addition, I have utilized Module Review to get some seniors' opinions about the module in which I am interested in. Lastly, I also perform bid points management by studying the past successful bid points. The module plan is reviewed regularly each semester as there may be timetable clashes and the introduction/removal of modules. I was really glad that I have a module plan as it has made my SEP module planning more flexible. I was able to take modules from many departments as I have meet the pre-requisite for various level 2 modules before the start of SEP through my careful planning.

The following are the list of modules in which I have taken:

ACADEMIC YEAR 2009/2010 SEMESTER 1

GEM2900 UNDERSTAND'G UNCERTAINTY & STATS THINK'G

MA1505 MATHEMATICS I

PC1141 PHYSICS I

PC1142 PHYSICS II

SP1201P FRESHMAN SEMINAR

ACADEMIC YEAR 2009/2010 SEMESTER 2

EC1301 PRINCIPLES OF ECONOMICS

LSM1301 GENERAL BIOLOGY

MA1506 MATHEMATICS II

PC1143 PHYSICS III

PC1144 PHYSICS IV

ACADEMIC YEAR 2010/2011 SEMESTER 1

EC2101 MICROECONOMIC ANALYSIS

MA1104 MULTIVARIABLE CALCULUS

PC2130 QUANTUM MECHANICS I

PC2131 ELECTRICITY & MAGNETISM I

PC2132 CLASSICAL MECHANICS

ACADEMIC YEAR 2010/2011 SEMESTER 2

EC2303 FOUNDATIONS FOR ECONOMETRICS

PC2193 EXPERIMENTAL PHYSICS I

PC2230 THERMODYNAMICS AND STATISTICAL MECHANICS

PC3130 QUANTUM MECHANICS II

SSS1207 NATURAL HERITAGE OF SINGAPORE

ACADEMIC YEAR 2011/2012 SEMESTER 1

PC4130 QUANTUM MECHANICS III

PC3193 EXPERIMENTAL PHYSICS II

PC3231 ELECTRICITY & MAGNETISM II

PC4248 GENERAL RELATIVITY

PC3288 ADVANCED UROPS IN PHYSICS I

ACADEMIC YEAR 2011/2012 SEMESTER 2 (University of Toronto)

PHY491H1  CURRENTINTERPRETATIONS OF QUANTUM MECHANICS
PHY450H1:  RELATIVISTIC ELECTRODYNAMICS
PHY357H1:  NUCLEAR ANDPARTICLE PHYSICS
PHY354H1:  ADVANCEDCLASSICAL MECHANICS
PHY358H1:  ATOMS, MOLECULESAND SOLIDS

Wide Module Selection

I have chosen to take level one exposure modules early in my university life so as to widen the range of modules that I can take. EC1301, which is the only level 1 economics module, has also allowed to take several other economics modules. MA 1505 and MA1506, which is part of my major requirements, has allowed me to use many level 2 and 3 MA modules as my backup modules every semester. This is very helpful for SEP module planning as I can take modules from 3 different departments (Physics, Maths and Economics). However, I still choose to take physics modules as I hope to take as many theoretical physics modules as possible.

SSS1207 Essay Sample

2011-07-27T20:59:00.015+08:00

DISCLAIMER: THE AUTHOR HAS TRIED HIS BEST TO ACKNOWLEDGE ALL THE SOURCES USED. THIS ESSAY IS MEANT TO BE A REFERENCE FOR SSS1207 STUDENTS. IT IS BY NO MEANS A BENCHMARK FOR A GOOD SSS1207 ESSAY.

“There is no need to protect Singapore's natural heritage as one can always travel to nearby countries like Malaysia and Indonesia to enjoy the goods and services of biodiversity”. Discuss.

Being a small but highly populated, Singapore has been facing a chronic shortage of land. Every hectare of land matters to us as it can ease the overarching demand of land for economic development and housing. In view of this, some argue that keeping our local nature sites is a waste of land as one can always travel to nearby countries like Malaysia and Indonesia to enjoy the goods and services of biodiversity. Indeed, having access to the goods and services from the pristine and rich biodiversity in these neighbouring countries[1] makes the natural habitats in Singapore seem redundant. However, our natural heritage possesses several characteristics which cannot be simply substituted by alternatives in other countries. Hence in my paper, I will be arguing that Singapore’s natural heritage should be protected to maintain a high quality of life. In this paper, natural features belonging to the natural environment which has been passed down since primeval Singapore shall be considered as natural heritage of Singapore[2]. Natural heritage, also known as the biodiversity, encompasses all the living organisms.

One of the compelling reasons for the protection of our own natural heritage is the regulating services[3] that it provides, such as the maintenance of air and water quality[4], which we cannot enjoy from the biodiversity of neighbouring countries. As Singapore seeks to reduce reliance over foreign water supply, there is growing emphasis on the catchment management to ensure a sustainable water supply[5]. The forest ecosystem surrounding our reservoirs[6] plays a significant role in the maintaining high water quality in our reservoirs. They help in the filtration of watershed’s water. Forests also help to improve the air quality by intercepting airborne particles and absorbing pollutants[7]. Keeping the air clean is essential for attracting and retaining talents. According to Hudson poll[8], Hong Kong is a less favourable relocation destination for executives than Singapore due to Hong Kong’s air pollution problem. Apparently, only the nature areas on Singapore can allow us to enjoy these free, location-specific regulatory services.

In a globalised world, borders matter less and identity may matter more. Thus, it is imperative that we contemplate what makes Singapore the special place called home. Our natural heritage can help to contribute a sense of identity and place[9]. Singaporean can take pride in knowing that we have a rich biodiversity despite our miniscule geographic size. Singapore, being 0.2% the size of UK, actually has some 360 species of birds or 60% of the number of species found in the UK[10]. In addition, researchers still regularly uncover some species new to science in a country as urbanized as Singapore, such as Johnson’s freshwater crab[11]. These distinctive features of our nature heritage are uniquely Singapore and it contributes a sense of identity in our people. In fact in the URA Lifestyle Survey 2009[12], 90.9% of the respondents agree that greenery contributes strongly to Singapore’s identity. Sense of place[13] is a feeling that a community is distinctively different from anywhere else. Globalization has caused societies to become more homogeneous and thus resulted in a loss of a sense of place. Our inhabiting places can act as an aide-memoire[14] to relive valued personal and family memories and hence help to create an emotional attachment to the place. As Singapore’s physical landscape is constantly changing, the seemingly static nature sites can serve as green landmarks to offer a sense of place.

Singapore’s biodiversity is beneficial to the physical, mental and social well being of Singaporeans. Research has shown that people living in areas with more green spaces[15] experience better general health. Natural areas are actively pursued by people to relieve the stresses[16] of everyday life in today’s fast-paced and high-stress society. Furthermore, the aesthetics and tranquillity of the natural environment is said to improve various dimensions of mental wellbeing[17] such as better cognitive performance[18]. In order to gain a competitive edge in retaining talents, Singapore’s physical environment should support this avenue of relaxation and mental refreshment. Green spaces also encourage more social interactions across different ethnic groups[19], facilitating intimate social relationships among people. This form of social cohesion is an essential part of social wellbeing. Given the multi-dimensional positive impacts of nature on wellbeing, it is not a surprise that the respondents of the URA Lifestyle Survey[20] agree that having green spaces are an important aspect of quality of life. What Singaporeans would really want is a physically, mentally and socially healthy home where they can live, work and play in.

Our natural heritage is huge capital asset[21] that can be tapped through bioprospecting. Bioprospecting[22] is the systematic search of chemistry compounds, genes and other valuable natural products. The different species in Singapore are like a treasure trove of resources for pharmaceutical and biotechnological purposes. One of the successful stories is the development of a commercial bacterial test kit by studying gene responsible for the clotting factor coagulogen found in mangrove horseshoe crab’s blood[23]. The discovery of a compound in the blue-green algae from Pulua Hantu[24] that kills cancer cells is another good illustration of the potential biomedical uses of our natural heritage. Destroying our biodiversity may result in the loss of undiscovered goods and services which are potentially useful.

By setting aside a piece of nature site, we would have to forgo any form of economic development on that piece of land. This may result in a less stellar performance on the economic scorecard. The preserved nature heritage would in turn provide a higher quality of life and overall wellbeing of our residents. Undeniably, the biodiversity of our neighbouring countries are almost indispensable in the provision of certain basic services such as timber. However, those foreign biodiversity can neither give us a sense of identity nor the localized regulatory services that we desire. We should aim to reap the greater dividends of the multi-functionality of our natural heritage, rather than performing a one-time economical conversion of these valuable inheritances. It is our responsibility to maintain and sustain the natural heritage. Any damage done to our biodiversity will be permanent.

[Word count: 999]

References

1. Asean Centre for Biodiversity. (unknown). Frequently Asked Questions about Biodiversity. Retrieved March 25, 2011 from http://www.aseanbiodiversity.org/index.php?option=com_content&view=article&id=341&Itemid=175.
2. United Nations Educational, Scientific and Cultural Organisation. (unknown). Convention Concerning the Protection of the World Cultural and Natural Heritage. Retrieved March 28, 2011 from http://whc.unesco.org/archive/convention-en.pdf.
3. Millennium Ecosystem Assessment. (2003). Ecosystems and Wellbeing: A framework
for Assessment. Retrieved March 25, 2011 from http://www.maweb.org/en/index.aspx.
4. Tan, H.T.W., Chou, L.M., Yeo, D.C.J., Ng, P.K.L. (2010). The Natural Heritage of Singapore (3rd ed.). Singapore: Prentice Hall.
5. Tortajada C. (2008). Water Management in Singapore. Water Resources Development. Vol. 2. No. 2. 227–240.
6. A Guide to Freshwater Fishes in Singapore. (unknown). Freshwater Fishes and the Singaporean. Retrieved March 29, 2011 from http://habitatnews.nus.edu.sg/guidebooks/freshfish/index.htm.
7. Julian. W. (2000). The Value of Trees. Wetlands. Vol. 7. No.3.
8. Hudson. (unknown). Pollution a Major Barrier to Attracting Top Talent to Hong Kong, According to Study. Retrieved March 25, 2011 from http://hk.hudson.com/documents/emp_asia_Press_Release_Air_Pollution_effecting_HK.pdf.
9. Henwood, K. (2003). Environment and health: is there a role for environmental and countryside agencies in promoting benefits to health, Issues in health development, NHS.
10. Ministry of the Environment and Water Resources. (2009). A Liveable and Lively Singapore: Strategies for Sustainable Growth. Retrieved March 25, 2011 from http://app.mewr.gov.sg/data/ImgCont/1292/sustainbleblueprint_forweb.pdf.
11. Tan, H.T.W., Chou, L.M., Yeo, D.C.J., Ng, P.K.L. (2010). The Natural Heritage of Singapore (3rd ed.). Singapore: Prentice Hall.
12. Urban Redevelopment Authority. (2010). URA Lifestyle Survey 2009. Retrieved March 29, 2011, from http://spring.ura.gov.sg/conceptplan2011/consultation.cfm.
13. Stokes, S. M., Watson, A. E. and Mastran, S. S. (1997). Saving America’s Countryside: A Guide to Rural Conservation (2nd ed.).Baltimore: Johns Hopkins University Press: 192.
14. Korpela, K. M. (1989). Place-identity as a product of environmental self regulation. Journal of Environmental Psychology. 9. 241-256.
15. De Vries, S., Verheij, R., Groenewegen, P. & Spreeuwenberg, P. (2003). Natural environments-Healthy environments? An exploratory analysis of the relationship between green space and health”. Environment and Planning. 35. 1717-1731.
16. Mace, B., Bell, P. & Loomis, R. (1999). Aesthetic, affective, and cognitive effects of noise on natural landscape assessment. Society and Natural Resources. 12:3. 225-242.
17. Kweon, B,. Sullivan, W. & Wiley, A. (1998). Green common spaces and the social integration of inner-city adults. Environment and Behavior. 30. 832-858.
18. Hartig, T., Evans, G., Jamner, L., Davis, D. & Garling, T. (2003). Tracking restoration in natural and urban field settings. Journal of Environmental Psychology. 23.109-123.
19. Ward Thompson, C. (2002) “Urban open space in the 21st century”, Landscape & Urban Planning, 60, 59-72.
20. Urban Redevelopment Authority. (2010). URA Lifestyle Survey 2009. Retrieved March 29, 2011, from http://spring.ura.gov.sg/conceptplan2011/consultation.cfm.
21. Gretchen C. Daily et al. (2000). The Value of Nature and the Nature of Value. Science. Vol. 289. 5478. 395-396.
22. Farmlandgrab.org. (1999). 7788 Biodiversity law. Retrieved March 29, 2011, from http://www.grain.org/brl_files/costarica-biodiversitylaw-1998-en.pdf.
23. Ding J.L., Ho B. (2001). New Era in Pyrogen Testing. Trends in Biotechnology. Vol. 19. 277 – 281.
24. Kesava, S. (2008, August 9). Found in Singapore: A new species of sponge. The Straits Times. Retrieved March 29, 2011, from http://www.tmsi.nus.edu.sg/found-in-singapore-a-new-species-of-sponge.

Risk Taking - Odds (Part II)

2011-07-27T14:43:00.011+08:00

DISCLAIMER: I AM NOT PROMOTING GAMBLING! BUT IF YOU REALLY CHOOSE TO GAMBLE, DO IT RESPONSIBLY!

In this article, I will teach you how to interpret a set of European odds?

For learning purpose, I shall use a coin-flipping game. There are only one bookmaker and one punter in this example. The coin used is believed to be fair and hence the chance of showing a head is the same as the chance of showing a tail. Lastly, we also assume that the bookmaker is not out to make money or lose money after many rounds of coin-flipping game.

The most rational set of odds set by the bookmaker will be 2 for Head and 2 for Tail. It means that if punter bet Head and the coin indeed shows Head, the punter will win $1 for every $1 the punter bets. However, if the coin shows Tail, the punter will lose every dollar that the punter bets. Why is the odd set at 2? It is because the probability of showing Head for a fair coin is ½. Over a long run, the bookmaker has 50% chance of losing the bet and 50% chance of winning the bet. If the bookmaker loses the bet, the bookmaker will lose $1 for each $1 bet placed by the punter. If the bookmaker wins the bet, the bookmaker will win $1 for each $1 bet placed by the punter. Over the long run, the expected gain by the bookmaker = ½(-$1)+1/2(+$1) = $0 for every dollar betted. This is what the bookmaker wants – not making or losing money after many games.

In fact, if the odds for Head = 1/x and the odds for Tail = 1/y, it means that bookmaker BELIEVES that the chances of the coin getting Head is x and the chance for Tail is y.

So, in what situation should a rational person enter the game and place the bet?

A smart punter will enter a game if the punter does not agree with the probabilities that the bookmakers believe. If punter somehow manage to get the coin to show Tail all the time (without alerting the bookmaker), it means that the punter believes that the probability of Tail =1. As the foolish bookmaker still thinks that the coin is fair, he/she will still believe that probability of Tail =1/2 (despite using an unfair coin). The smart punter will definitely enter the game and bet on Tail. Over the long run, the expected return of the punter is 1(+$1)+0(-$1) = $1 for every dollar betted. The smart punter is better off by betting. However, the smart punter will stay out from betting Head as probability of Head perceived by bookmarker > probability of Head perceived by the smart punter. The punter will be worse off betting Head as the expected return will be 0(+$1)+1(-$1) = -$1 per dollar betted.

In the next article, I will discuss about bookmaker’s rule and the non-existence of arbitrage in a single betting game if the bookmaker is rational.

GeoGebra Training Manual Part IX

2011-07-20T19:45:00.001+08:00

IX. Sketching a Cumulative Frequency Curve

Objective: To draw a cumulative frequency curve for the height of 8 plants.

GeoGebra Training Manual Part VIII

2011-07-20T19:34:00.009+08:00

VIII. Advanced Features for Curve Sketching

Objective: To obtain the roots of equation, turning points and line of symmetry for a quadratic curve.

Suggested Topics: Roots of quadratic equation, Turning points of a curve, Symmetry in graph.

1. Deleting the point A

- We will continue to use the previous construction for this exercise.

- Delete point A by right-clicking on point A and select the Delete option.

2. Finding the roots of the curve

- The INPUT BAR can also be used to enter commands. The list of commands can be found in the pull-down menu which can be found at the bottom right hand corner of the GeoGebra window.

- To find the root of the equation, select the Root command. . Notice that something appears that the INPUT BAR. Edit the command to Root[f] and then press Enter.

- You have just requested the software to find the roots of the curve f(x).

- Hint: the commands in the pull-down menu are arranged in alphabetical order.

3. Displaying roots of equation

- Go insert textbox and enter “root 1= “+x(A) . Insert another textbox and enter “root 2=

“+x(B)

- Note: x(A) denotes the x-coordinate of point A while y(A) denotes the y-coordinate of point A.

4. Finding the turning point

- To find the turning point, select Extremum from pull-down list for commands. Inside the bracket [], insert the letter f. It is to tell the software to locate the turning points for f(x). For this case, the turning point is labelled as point C on the DRAWING PAD.

- Hint: If you do not know what are required within the brackets of a certain command, press key F1. A pop-up window appears explaining the syntax and necessary parameters of the command.

5. Displaying the turning point

- Insert textbox and enter “turning point = ”+C . Adjust the font size of the textbox to increase its visibility.

6. Line of symmetry

- From the TOOLBAR, click on the 4th icon and select Parallel Line tool. Make use of the TOOLTIP to help you draw the vertical line of symmetry for f(x).

- Hint: The line of symmetry is parallel to the y-axis and passes through point C.

- Change the line of symmetry into a dotted line by going to the Style tab of the Properties Dialog and change Line Style.

GeoGebra Training Manual Part VII

2011-07-20T19:26:00.006+08:00

VII. Drawing of a Quadratic Curve

Objective: To plot a quadratic curve in form a(x-h)2+k, where a, h and k can be varied using a slider. The slope of the tangent of the curve

Suggested Topics: Quadratic equations, Curve transformation, Concepts of differentiation

1. Preparation

- To prepare for the curve sketching, turn on the axes.

- The axes can be turned on by clicking on View -> Axes once.

- You may want to turn on the Grid by clicking on View -> Grid once.

2. Labeling of Axes and Origin

- You may want to label the axes and origin so to model the way. . Right-click anywhere on the Drawing Pad and select Graphics View to include the label of the xAxis and yAxis.

- You can include the origin by adding a new point at (0,0) and then re-label it as O.

3. Adding slider for a, h and k

- On the TOOLBAR, select the 10th icon and then click on the Slider tool and click on the DRAWING PAD. After clicking on the Drawing Pad, slider pop-out window will appear. Enter ‘a’ as the Name. Set the min at -10 and set the max at 10. Allow the Increment to be at 0.1.

. Repeat for h and k.

4. Inserting the equation

- Enter f(x) = a*(x-h)^2+k into the INPUT BAR.

- Note: you can also enter y = a*(x-h)^2+k as the equation.

- Tip: You can also include the superscript 2 by selecting it from the pull-down menu on the right on the INPUT BAR.

5. Point A on the curve

- We require a point on the curve before can draw a tangent to the curve.

- Add a new point A on the curve by selecting the New Point tool.

6. Adding a tangent to the curve at Point A

- Go the TOOLBAR, click on the 4th icon and select the Tangent tool. Next, click on point A, followed by the curve. You will obtain a tangent passing through point A.

7. Slope function

- Click on the 8th icon (from the left) on the TOOLBAR and select the Slope tool. Next, click on the tangent line.

8. Enlarging the point A

- You may want to the enlarge the point A to allow your students to see that point more clearly.

- To do so, right-click to open up the Properties Dialog. Go to the Style tab and increase Point Size by dragging the pointer to the right.

9. Displaying the equations of the lines

- Right click on the quadratic curve and select Object Properties. Check Show Label and select Value on the drop down menu on the right. Click Close after this.

GeoGebra Training Manual Part VI

2011-07-20T19:19:00.007+08:00

VI. Drawing of a Straight Line Graph

Objective: To construct a linear graph in where the gradient and the y-intercept can be varied through the use of sliders. The slope of the line is also generated.

Suggested Topics: Linear graphs, Simultaneous equations

1. Preparation

- To prepare for the curve sketching, turn on the axes.

- The axes can be turned on by clicking on View -> Axes once.

- You may want to turn on the Grid by clicking on View -> Grid once.

2. Labeling of Axes

- It is important to label the axes to make sense of the graph.

- Right-click anywhere on the Drawing Pad and select Graphics View. For the xAxis tab, select x from the Label pull-down menu. For the yAxis tab, select y from the Label pull-down menu.

3. Labeling the origin

- You can label the origin by selecting the New Point tool. Hover the mouse over the (0,0) location and then click on it. A black dot will appear.

- To rename of the point quickly, select the Move tool and click on the new point. Immediately, press ‘O’ on the keyboard. You will see a pop-out window prompting you for the new name.

4. Introducing m and c

- As we need use these two unknown parameters, we need to define them. A way to ‘define’ them is to form a slider.

- On the TOOLBAR, select the 10th icon and then click on the Slider tool and click on the Drawing Pad. After clicking on the Drawing Pad, slider pop-out window will appear. Enter ‘m’ as the Name. Set the min at -10 and set the max at 10. Allow the Increment to be at 0.1.

- Repeat for c.

5. Insert equation

- The equation can be entered into the INPUT BAR that can be found at the bottom left corner of the GeoGebra window.

- Enter y=m*x+c into the INPUT BAR.

- Do not worry if you do not see the graph. Try playing with the slider and you will find your

graph! . Hint: Do remember to enter * whenever there is a multiplication of parameters/variable. Alternatively, you can also replace * with a spacing in between m and x.

6. Slope function

- Click on the 8th icon (from the left) on the TOOLBAR and select the Slope tool. Next, click anywhere on the straight line graph.

- A coloured triangle and two corresponding numbers will appear. One of the numbers is always 1 while the other one reflects the slope of the graph.

7. Addition line y=-1

- At the INPUT BAR, key y=-1 and then press Enter key on your keyboard.

8. Points of intersection between two lines

- To find the points of the intersection, click on the 2nd icon on the TOOLBAR and select Intersect Two Objects tool.

- Use the TOOLTIP (or some logic) and you will be able to find out what you should click after selecting the tool. You will get a black dot at the intersection point.

9. Displaying the point of intersection

- The points of intersection can be displayed clearly by inserting a textbox.

- Click on the 10th icon on the TOOLBAR and select the Insert Text tool. Next, click on the place where you want the textbox to be. Enter "Intersection Point = " + A into the field of the pop-out window.

- Tip: Everything inside “” belongs to the static component of the textbox while +A belongs to the dynamic part of the text.

10. Displaying the equation of the line

- Right click on the straight line and select Object Properties. Check Show Label and select Value on the drop down menu on the right. Click Close after this.

GeoGebra Training Manual Part V

2011-07-20T19:08:00.004+08:00

V. Introducing the Slider

Objective: Recap the important objects of geometric construction. Sliders will be introduced to adjust the length of a line and angle. Static and dynamic text will also be introduced.

Possible Extensions: Rotation, Curve Sketching, Trigonometric functions, etc.

1. Preparation

- To prepare for geometry construction, we shall close the ALGEBRA VIEW and turn off the axes from the DRAWING PAD.

2. Adding a slider

- On the TOOLBAR, select the 10th icon and then click on the Slider tool and click on the DRAWING PAD.

3. Customizing the slider

- After clicking on the DRAWING PAD, Slider pop-up window will appear. For the Basic tab, enter 0 as the min and 5 as the max. For the Slider tab, select Vertical for the pull-down menu. Lastly, click on Apply and you will obtain a vertical slider.

4. Inserting line with length a

- On the TOOLBAR, click on the 3rd icon (from the left) on the TOOLBAR and select Segment with Given Length from Point. Next, click anywhere on the DRAWING PAD. Point A will appear. Enter ‘a’ into the pop-out window and then press OK.

5. Adding another slider

- On the TOOLBAR, select the 10th icon and then click on the Slider tool. Next, click on the Drawing Pad and the slider pop-out window will appear. On the Basic tab, select Angle radio button. Set 0° as the min and 360° as the max. Also, set the increment at 1°. For the Slider tab, select Horizontal from the pull-down menu. A horizontal slider will thus be obtained.

6. Inserting an angle with given size

- First, click on the 8th icon (from the left) on the TOOLBAR and select the Angle with Given Size tool. Next, click on leg point (point B) and then click on the vertex (Point A). Enter ‘a’ for the size of angle and select counter clockwise.

- Recall: The Greek letters can be found from the pull-down menu at the right hand side.

7. Connecting AB’

- Using the Segment between Two Points tool, connect A to B’

- Note: the length of AB is always equal to the length of AB’.

8. Length of line segment AB

- To find length of line segment AB, use the Distance or Length tool.

- Utilize the TOOLTIP to help you in recalling what to click after selecting this tool.

9. Decorating the slider

- We want to change the colour of the slider to enhance the appearance.

- Right-click on any of the sliders to open the Properties Dialog. On the Colour tab, select your favourite colour for your slider.

- The thickness of the slider can also be varied by going to the Style tab and drag the pointer.

- All these will make the slider more outstanding.

10. Using the slider

- The length of the line and the angle can be varied by adjusting the slider.

- Click on the Move tool and then drag the circular dot along the slider. Observe the change in the length of the line AB and the angle between AB and AB’.

- Hint: The arrow cursor will change into a hand-like cursor if you successfully in selecting the circular dot. The circular dot will also become bigger (see figure on the right).

11. Inserting title (Static Text)

- You may want to include a title to construction. This can be done by adding a textbox.

- Click on the 10th icon (from the left) on the TOOLBAR and select the Insert Text tool. Next, click somewhere on the DRAWING PAD in which you want the title to be at.

- A text pop-up window will appear. Enter the title that you prefer and then click OK.

- You can move the textbox around using the Move tool.

- Static text: The content in the textbox is not affected by existing objects and adapts

automatically to modifications.

12. Displaying Coordinates of B (Static and Dynamic Text)

- Click on the 10th icon (from the left) on the TOOLBAR and select the Insert Text tool. Next, click the place you want the title to be at. A text pop-out window will appear.

- Enter the static component: B’ =. Then, click on the point B’ on the Drawing Pad. Notice the

changes in the Text field. Press OK.

- Adjust the values of the sliders and observe the values of the B’ coordinates being displayed.

- Dynamic text: The content in the textbox is affected by existing objects and adapts automatically to modifications.

13. Changing the size of the font

- We want to make the title more prominent by increasing the font size.

- Right-click on the title textbox and open Properties Dialog. Choose the Text tab. Select your desired font size by clicking on the pull-down menu.

- Unfortunately, the selection of fonts is very limited in GeoGebra.

GeoGebra Training Manual Part IV

2011-07-18T21:20:00.004+08:00

IV. Practice

Objective: Construct diagram to consolidate your learning.

Applications: Setting of geometry examination question

1. Construction protocol

- It is common that you may find an interesting or useful GeoGebra file online and you may want to know how it is something constructed. All these information is summarised in the construction protocol.

- To access the construction protocol, on the MENU LINE click View -> Construction Protocol.

2. Export the Picture to Clipboard

- GeoGebra will export the whole DRAWING PAD into the clipboard. Thus, you need to make the GeoGebra window smaller in order to reduce unnecessary space on the DRAWING PAD.

- This can be done by moving your figure (or the relevant section) to the upper left corner of the DRAWING PAD using the Move tool. You might want to use tools Zoom In and Zoom Out in order to prepare your figure for the export process. Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse.

- To copy the construction, click File -> Export -> Graphic View to Clipboard. Lastly, paste your graphic file into your word processing program.

3. Angle with given size

- The above practice can be done accurately with the help of the Angle with Given Size tool.

- First, click on the 8th icon (from the left) on the TOOLBAR and select the Angle with Given Size tool. Next, click on leg point (see figure below) and then click on the vertex. Set the desired size of angle and direction (clockwise or counter clockwise) in which the angle will run from the leg.

- Tip: The figure shows 45 degrees clockwise angle formed. The leg point and the vertex are also shown for clarity.

4. Adding Caption

- If you have difficultly constructing the diagram accurately, we can also make use of Caption function. It allows us to label angles according to our preferences without worrying about the true angle value of our construction.

- Right-click on the angle that you want to add caption to. Open the Properties Dialog and select the Basic tab. Check Show Label and click Caption in the pull-down menu. Next, enter your prefered caption.

- Tip: If you require the degree symbol (°), click on the pull-down menu just next to the field. It is the 3rd symbol.

GeoGebra Training Manual Part III

2011-07-18T21:07:00.011+08:00

III Construction of Alternate Angles inscribed in a Circle

Objective: To construct alternate angles inscribed in a circle.

Suggested Topics: Alternate angles, Vertically opposite angle, Corresponding angle, Circle Theorem

1. Preparation

- Close the ALGEBRA VIEW window by clicking on View and uncheck Algebra View while the axes can be removed by clicking on View -> Axes once.

2. Labeling

- To label the objects, on the MENU LINE click Options -> Labelling -> All New Objects.

3. Insert Point A

- Click on the 2nd icon (from the left) on the TOOLBAR and select the New Point tool. Next, click at the middle of the DRAWING PAD.

4. Re-label the point as O

- We want to change the name of the new point.

- Right–click on that point and select Object Properties. Select the Basic tab and enter O in the Name input field. Then, close the Properties Dialog.

5. Draw circle with radius 4 units

- Click on the 6th icon (from the left) on the TOOLBAR and select the Circle with Centre and Radius tool. Click on the point O to indicate that it will be the centre of the new circle, and fill in the 4 units as radius in the pop‐up window.

6. To draw chord AB

- Click on the 3rd icon (from the left) on the TOOLBAR and select the Segment between Two Points. Place your cursor near the edge of the circle. If the cursor is located right above the circumference of the circle, the cursor will change from a crosshair into a white arrow. Next, click at the circumference of the circle to form point A and extend the line segment to another part of the circumference. Once again, you will only click to create point B when your cursor becomes a white arrow.

- Putting down the points only when there is a change in cursor appearance will ensure that the points plotted are really bounded to the circumference of the circle. (Try moving points A and B using the Move tool, which is the 1st icon of the TOOLBAR.)

7. Insert Point C

- Click on the 2nd icon (from the left) on the TOOLBAR and select the New Point tool. Next, click on somewhere on the circumference of the circle.

- Do remember to look out for the change in cursor.

8. Draw line passing through C and parallel to chord AB

- Click on the 4th icon (from the left) on the TOOLBAR and select the Parallel Line tool. Then, click on point C and then click on the line AB. The line created will pass through point C and is parallel to chord AB.

9. Using the TOOLTIP

- You may be wondering how to remember what to click after selecting the appropriate tool. Fortunately, whenever you select any of the tools on the TOOLBAR, a TOOLTIP will appear on the TOOLBAR to help you in using that tool.

10. Point of Intersection D

- Click on the 2nd icon (from the left) on the TOOLBAR and select the New Point tool. Next, click on the place where the circle and the line meet to form point D.

11. Line segments AD, BC and CD

- Click on the 3rd icon (from the left) on the TOOLBAR and select the Segment between Two Points. Connect point A and point D together using a line segment. Connect point B and point C together to form another line segment. Lastly, connect point C and D up to form a line segment.

- We require line segment AD as we will hide the parallel line CD later.

12. Hide line CD and keep line segment CD

- Right-click on the line CD and click on Show Object. The line CD will not appear on the DRAWING PAD.

- Tip: Right-click outside the circle so as to avoid selecting the line segment CD.

13. Properties Dialog

- We need to open up the Properties Dialog in order to decorate the lines. On the MENU LINE, click on Edit -> Object Properties.

- Observe what is so special about Line b on the left frame of the Properties Dialog. The dot is not shaded for Line b and this actually indicates that Line b is being hidden up.

14. Decorating line segment AB and CD with parallel line marks

- Select the correct Segment label representing line segment AB at the left frame of the Properties Dialog. Choose the Decoration tab and select your favourite parallel line marks. Select the correct Segment label representing line segment CD from the left frame of the Properties Dialog. Next, choose the same parallel line marks used for line segment AB.

15. Labeling Angle BAD

- Let us first learn how to label angle BAD. Click on the 8th icon (from the left) on the TOOLBAR and select the Angle tool. Next, click on line segment AD and AB. This is to tell the software that we want to label the angle that is enclosed by line segment AD and AB.

16. Removing reflex angle

- Due to the convention set by the software, you may also get a reflex angle instead of an acute angle.

- To remove the reflex angle, right-click on the angle and select Object Properties. Go to the Basic tab and uncheck Allow Reflex Angle.

17. Labeling Angle ABC, ADC, BCD

- There is another way of generating angles. Click on the 8th icon (from the left) on the TOOLBAR and select the Angle tool. As mentioned by the TOOLTIP, you can also use 3 points to define the angle. If you want to create angle ABC, click on point A, B and then point.

- Repeat for angle ADC, BCD. Remove the reflex angles by unchecking Allow Reflex Angle in the Properties Dialog.

18. Showing alternate angles

- Try moving point A, B or C after clicking on the Move tool. This construction can be used to show that alternate angles are equal.

GeoGebra Training Manual Part II

2011-07-18T20:44:00.018+08:00

II Construction of a Right Angle Triangle

Objective: To draw and decorate a right angle triangle ABC where the length of one leg AB is 5 units and the hypotenuse BC is 8 units. Find the area of the triangle and the length of side AC.

Suggested Topics: Trigonometry, Area of Triangles, Pythagoras' Theorem

1. Preparation

- To prepare for geometry construction, you should close the ALGEBRA VIEW and remove the axes from the DRAWING PAD.

- To close the ALGEBRA VIEW window, on the MENU LINE click View -> uncheck Algebra View. The axes can be removed by clicking on View -> Axes once.

2. Labeling

- To label the objects, on the MENU LINE click Options -> Labelling -> New Points Only. [ERROR: wrong diagram]

3. Drawing a line segment with length 5 units

- Click on the 3rd icon (from the left) on the TOOLBAR and select the Segment with Given Length from Point tool. Next, click anywhere on the DRAWING PAD. Point A should appear. Key in 5 into the pop-out window and then press OK.

4. Perpendicular line through A

- Click on the 4th icon (from the left) on the TOOLBAR and select the Perpendicular Line tool. Next, click on the Point A and then segment AB. A line perpendicular to segment AB passing through A should be formed on the DRAWING PAD.

- Tip: The line segment will appear thicker when the cursor is resting above the line. You can only select the line once the line appears thicker.

5. Moving and Zooming In/Out

- In order for the whole construction to fit nicely onto the DRAWING PAD, one may have to move the diagram or zoom in/out.

- To move the diagram, click on the 8th icon (from the left) on the TOOLBAR and select the Move Graphics View tool. Next, click on the DRAWING PAD in order to move the construction.

- To zoom out the diagram, click on the 8th icon (from the left) on the TOOLBAR and select the Zoom Out tool. The mouse cursor appears as a magnifying glass with a minus sign in the centre. Click on the DRAWING PAD to zoom out. If you have zoomed out excessively, use the Zoom In tool.

- Tip: One can also make use of the mouse scroll wheel to zoom in/out. Try it out!

6. Drawing a circle of centre B and radius 8 units

- To place the third corner of the triangle, you use one of the circle tools. Click on 6th icon (from the left) on the TOOLBAR and select the Circle with Centre and Radius tool. Click on the point B, and fill in the 8 units as radius in the pop-out window.

- The length of the hypotenuse is equal to the radius of the circle.

7. Intersection of the perpendicular line and circle

- GeoGebra does not register any intersection between the circle and perpendicular line although it appears to us that the circle and perpendicular line do intersect. Hence, we need to ‘create’ the intersection point to tell GeoGebra that there is indeed an intersection between the circle and the perpendicular line.

- Choose 2nd icon (from the left) on the TOOLBAR and select Intersect Two Objects tool. Next, hover your cursor at the intersection point until both the circle and the perpendicular line are selected (becomes thicker). Click on intersection point and a solid black dot labelled C should be formed. Point C is also the third corner of the triangle.

8. Drawing a triangle

- We have already constructed the 3 points of the triangle. It is now time for us to connect the points together to form a single entity (triangle ABC).

- Choose the 5th icon (from the left) on the TOOLBAR and select Polygon tool. Click all the corners of the triangle in the anti-clockwise direction and close the polygon by connecting the last and the first vertex (e.g. A, B, C and A).

- The orange-coloured polygon is the required right angle triangle ABC.

9. Properties Dialog

- In order to customize triangle ABC, you need to open up the Properties Dialog. On the MENU LINE, click on Edit -> Object Properties.

- Tip: Properties Dialog is the pop-out window that allows us to change the properties of the objects.

10. Selecting line BC

- As we are interested in changing the colour of line BC, we need to first select line BC before changing its properties. On the left frame of the Properties Dialog, all the elements on the DRAWING PAD will be reflected there.

- Hover your mouse over the list of Segment indicated there and try to identify line BC. Next, select line BC by clicking on the label of the line. The picture on the right shows that Segment a1 has been selected.

11 Changing the colour of line AB

- Select the Colour tab that is located at the top of the Properties Dialog. Then select the desired colour. Close the Properties Dialog once you are done.

12. Undo the previous action

- You may regret changing the colour of line BC and you hope to undo the previous action. Click on Undo icon (pointing to the left) that is located at the top right hand corner of the GeoGebra window.

- Tip: You can also redo the previously undone action by clicking on the Redo icon (pointing to the right).

13. Hiding the unnecessary elements

- You may have realised that other than desired right angle triangle ABC, several other objects are also required in the process to aid in the construction. Hence, we need to hide them (in this example, perpendicular line and the circle) after the construction.

- First click on Edit ->Object Properties on the MENU LINE. Select the circle and go to the Basic tab. Next, uncheck the Show Object.

14. Saving the construction

- Once you are satisfied with the construction, you may want to save your construction. . Go to MENU LINE, click on File -> Save As. Key in your desired file name and click Save.

15. Find the area of triangle ABC

- To find the area of the triangle ABC, click on the 8th icon (from the left) on the TOOLBAR and select the Area tool. Next, click on the shaded area of the triangle.

- The area of the triangle ABC should be shown in a textbox.

16. Moving the area textbox

- The textbox indicating the area of triangle ABC will be appearing at an obscured position and thus you may want to move it to a better position.

- Click on the 1st icon (from the left) on the TOOLBAR and select the Move tool. The cursor will appear as a white arrow. Next, click and hold onto the textbox and drop it at a better location.

17. Find the length of AC

- To find the length of AC, click on the 8th icon (from the left) on the TOOLBAR and select the Distance or Length tool. Then, click on side AC and the length of AC will appear in a textbox.

GeoGebra Training Manual Part I

2011-07-18T20:24:00.012+08:00

I. Introduction to GeoGebra User Interface

Objective:

To familiarise with GeoGebra’s user interface by viewing a video

Source:

GeoGebra - Overview: http://www.youtube.com/watch?v=A5GkiA8WDSw

Important thing to take note of:

For window user: in the video, all clicks are referred to the left click of the mouse, unless otherwise specified.

Synopsis of the video:

1. Main Components of GeoGebra

- DRAWING PAD

- ALGEBRA VIEW

- INPUT BAR

- TOOLBAR

- TOOLTIP

- MENU LINE

- ALGEBRA VIEW: Keep track of the objects (also called as elements) on the DRAWING PAD

2. Labeling of the objects

3. Use of INPUT BAR

- Standard mathematical symbols and special functions

- Greek letters

4. Commands

5. Use of TOOLBAR

- If the top of the icon is clicked, whatever tools shown are selected.

- If the bottom of the icon is clicked, a list of the available tools is displayed along with the tool’s name. Note that a red arrow will appear if your cursor is hovering near the bottom of the icon.

6. Types of objects

- Free objects (free to move around)

- Dependent objects (restricted by other objects)

7. Line tools (3rd icon from the left)

- Line through 2 points tool

- Ray through two points tool

8. Circle tools (6th icon from the left)

- Circle with Centre through Point tool

- Compass tool

9. View menu

GeoGebra Training Manual

2011-07-18T20:14:00.016+08:00

* GeoGebra is equivalent to Geogebra or geogebra

Content

I Introduction to GeoGebra User Interface

II Construction of a Right Angle Triangle

III Construction of Alternate Angles inscribed in a Circle

IV Practice

V Introducing the Slider

VI Drawing of a Straight Line Graph

VII Drawing of a Quadratic Curve

VIII Advanced Features for Curve Sketching

IX Sketching a Cumulative Frequency Curve

Prepared by: Jeysthur Ang

Guided by: Teng Jun Yuan

Introduction

This training manual aims to introduce and familiarize maths teachers with the essential components of GeoGebra. At the end of the two sessions, the teachers should be more confident and competent in utilising GeoGebra as learning enabler in geometry and graph-drawing classes.

Why GeoGebra?

- Sheer wealth of free educational resources hosted on GeoGebra Wiki

- GeoGebra User Forum: a platform for users to seek advice from the GeoGebra community

- Can form HTML interactive worksheet

- Most importantly, it’s FREE!

Useful Links

- GeoGebra Installer: http://www.geogebra.org/cms/en/installers

- GeoGebra Wiki: http://www.geogebra.org/en/wiki/index.php/English_UK

- GeoGebra Video Tutorials: http://www.youtube.com/geogebrachannel

- GeoGebra Help 3.2: http://www.geogebra.org/help/docuen/

- GeoGebra User Forum: http://www.geogebra.org/forum/

How to use this training manual?

- Crafted for self-directed learning, this training manual is concise without compromising on content and clarity. We strongly encourage you to perform the constructions while reading the manual concurrently.

- Words shown in the user interface are italicized. (E.g. New Point tool) - PENDING

- The main components of GeoGebra are in capital letters. (E.g. DRAWING PAD)