Recommended Maths Tuition Singapore

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Maths Tuition @ Bishan starting in 2014

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Cost of education in Singapore

Source: http://www.epigami.sg/blog/cost-of-education-in-singapore/

How much does it cost to educate a child in Singapore?

Answer: $80,940 or approximately 3 Round-the-World Trips!

Read more at: http://www.epigami.sg/blog/cost-of-education-in-singapore/

Release of O Level Results 2014

Sincerely wishing every student all the best for their O Level Results!

Meanwhile, all Secondary 3 to 4 students should start studying hard for their O Levels. 🙂

It has been many years since the release of my O Level Results. Sincerely wish my students to do well and even surpass me in their O Level Results.

maths-tutor-o-level-cert
Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.

O Level Maths Group Tuition at Bishan

Start Maths Revision Early for the Best Results!

O Level Group Tuition @ Bishan starting in 2014!

Maths is a subject that requires students to start revision / practice early!

It needs consistent practice and last minute studying is not going to work well!

Many students have the wrong concept that they can start practising questions one or two months before the O Levels. The problem is, without constant practice, the questions from the Ten Year Series would be too difficult for students to even begin attempting the questions! This is especially true for Additional Mathematics. This leads to panic and is not the desired study strategy. This is the main reason why it is possible to score very low (less than 20 marks out of 100) in Maths, if the student does not have solid foundation or has lack of practice. To avoid this scenario, start practicing and revising Maths now! Many students already start studying / learning in advance during the December holidays. January is still a good time to start! As the Chinese proverb states: “一年之计在于春一日之计在于晨”, the best time to begin planning for a task is in Spring.

Also, the current O Level Maths is not like the O Level of the past! Due to higher education standards nowadays, and competition from foreigners (especially China students whose pet subjects are Maths and Chinese), the bell curve for E Maths has shifted very very high. Rumours have it that 90 marks is necessary for a guaranteed A1 in E Maths.

On the bright side, it is very possible to improve in Maths with practice. Look at the Mathematics questions in O Levels, one long question is around 10 marks. Answering that one question correctly will already boost your score by 10 marks. (2 grades). Answering two long questions correctly will boost score by a whopping 20 marks!

Hesitate no longer! Start revising for your Maths now!

O Level Group Tuition @ Bishan starting in 2014!

Bishan-Ang Mo Kio area to get new JC in 2017

Source: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Bishan-Ang Mo Kio area to get new JC in 2017

The site for the new JC at the junction of Sin Ming Avenue and Marymount Road.
Lee Jian Xuan

Saturday, Jan 04, 2014

SINGAPORE – A new junior college that will open in 2017 for students from three Integrated Programme (IP) schools will likely be built on the site of the Asian Golf Academy near Bishan.

A statement on the Ministry of Education (MOE) website says the new campus will be at the junction of Sin Ming Avenue and Marymount Road, where the driving range is located.

The area is also zoned for an educational institution, according to the Urban Redevelopment Authority’s Draft Master Plan 2013.

Singapore’s 20th school to offer a JC programme will take in IP students from Catholic High School, CHIJ St Nicholas Girls’ School and the Singapore Chinese Girls’ School. It will also admit more than 100 students from other secondary schools who have completed their O levels.

It will be the newest JC since Innova JC in Woodlands was completed in 2005.

Read more at: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Secondary 4 O Level E Maths and A Maths Group Tuition, Bishan

https://mathtuition88.com/group-tuition/
https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

maths challenge

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to mathtuition88@gmail.com .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

The ideal Singapore JC subject combination for applying to Medicine

Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine

Source: http://sgforums.com/forums/2297/topics/439605

Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics

Source: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=40&t=12228

Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

Math is at the heart of physics. (O Level Maths and Physics Tips)

Source: http://www.academictips.org/acad/physic/physics_study_skills.html

Studying and practising Mathematics is one of the most useful things an O level student can do.

Not only are the two Maths (E Maths and A Maths) highly intertwined, studying Maths can actually help the students’ Physics too. There are some topics like Vectors and Kinematics in Physics that are also present in Mathematics.

Math is at the heart of physics. So the better your math, the better you’ll do in physics.

A good working knowledge of algebra and trigonometry is needed for Physics.

Mnemosyne with a mathematical formula.
Mnemosyne with a mathematical formula. (Photo credit: Wikipedia)

Recommended Maths Olympiad Books for Self Learning / Domain Test

Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain.

A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series)

The Art of Problem Solving, Vol. 1: The Basics

The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions.

GEP Math Olympiad Books

If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid!

A suitable book would be The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.

Other Suitable Math Olympiad Books for GEP

These are some books that are very popular and highly rated on Amazon.


Challenging Problems in Algebra (Dover Books on Mathematics)

Challenging Problems in Geometry (Dover Books on Mathematics)
Math Circles for Elementary School Students: Berkeley 2009 and Manhattan 2011 (MSRI Mathematical Circles Library)

My Best Mathematical and Logic Puzzles (Dover Recreational Math)
The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics)

The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)

Secondary 4 Maths Tuition @ Bishan starting in 2014.

https://mathtuition88.com/group-tuition/

https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

A-level Marks/Grade required to enter NUS

NUS Cut Off Points (COP)

Source: http://www.nus.edu.sg/oam/gradeprofile/sprogramme-igp.html

Table 1: Grade Profiles of the 10th and 90th percentiles of A-Level Applicants offered places for courses at NUS in Academic Year 2012-20132

NUS Courses

Representative Grade Profile 3H2/1H1

10th percentile
90th percentile
Faculty of Law
Law*
AAA/A
AAA/A
School of Medicine
Medicine*
AAA/A
AAA/A
Nursing*
BCC/C
AAA/C
Faculty of Dentistry
Dentistry*
AAA/A
AAA/A
School of Design & Environment
Architecture*
ABB/B
AAA/A
Industrial Design*
BBB/B
AAA/A
Project & Facilities Management
BBC/C
ABB/C
Real Estate
BBC/B
AAB/B
Faculty of Engineering
Engineering
ABB/C
AAA/A
Bioengineering
ABB/C
AAA/A
Chemical Engineering
AAA/B
AAA/A
Civil Engineering
BBC/B
AAA/B
Electrical Engineering
BCC/B
AAA/B
Environment Engineering
BBB/C
AAA/B
Engineering Science
BBB/C
AAA/A
Industrial & Systems Engineering
AAB/B
AAA/A
Materials Science & Engineering
AAB/B
AAA/A
Mechanical Engineering
ABB/C
AAA/A
School of Computing
Computing (Computer Science)
BBC/C
AAA/A
Computing (Information Systems)
BBB/C
AAA/B
Faculty of Engineering & School of Computing
Computer Engineering
BCC/B
AAA/B
Faculty of Science
Pharmacy
AAA/A
AAA/A
Science
BBC/B
AAA/A
School of Business
Business Admin
AAA/B
AAA/A
Business Admin (Accountancy)
AAA/A
AAA/A
Faculty of Arts & Social Sciences
Arts & Social Sciences
BBB/B
AAA/A
Arts & Social Sciences (MT related)
BBC/C
BBB/B
Environmental Studies
Environmental Studies
AAB/B
AAA/A

* Courses that require interview &/or test.

2 Double degrees are excluded from the table.

Chinese Math Students vs English Math Students

Source: http://toshuo.com/2007/chinese-math-students-vs-english-math-students/

This is a recent test used in England:

a diagnostic math test for first year university students in England

Here’s a Chinese math test:

a math question from a Chinese college entrance test

Now we know why students from China are so good at Maths!

Good night’s sleep adds up to better exam results – especially in maths

To all students taking Maths exams, do have a good night’s sleep before the exam!

Source: http://www.telegraph.co.uk/health/healthnews/5486844/Good-nights-sleep-adds-up-to-better-exam-results-especially-in-maths.html

Researchers found that higher scores were related to greater sleep quality, especially less awakenings rather than the actual length of time asleep.

The team of researchers, led by Dr Jennifer Cousins at the University of Pittsburgh, studied 56 adolescents and compared their sleep patterns with their exam grades.

They found those that enjoyed deeper, less disturbed, sleep were the most successful, especially in maths but also in English and history. 

Those who fell asleep and awoke easily – especially at weekends – were found to have better exam results.

Higher maths scores were related to less night awakenings, less time spent in bed, higher sleep efficiency and great sleep quality.

Formula to guess Month of Birthday from Singapore NRIC

Latest Update: We have created a JavaScript App to Guess Birthday Month from NRIC

Website: http://mathtuition88.blogspot.sg/2014/12/javascript-app-to-calculate-birthdate.html

Here is a Math Formula trick to have fun with your friends, to guess their Month of Birthday given their NRIC, within two tries.

(only works for Singapore citizens born after 1970)

The formula is: take the 3rd and 4th digit of the NRIC, put them together, divide by 10, and multiply by 3.

For an example, if a person’s NRIC is S8804xxxx, we take 04, divide by 10 to get 0.4

Then, 0.4 multiplied by 3 gives 1.2

Then, guess that the person is either born in January (round down 1.2 to 1) or February (round up 1.2 to 2). There is a high chance that you are right! Usually, round up for the first six months (Jan to Jun), and round down for the last six months (Jul to Dec).

This formula was developed and tested by me. There are some exceptions to the rule, but generally it works fine especially for people born from 1980 to 2000.

Hope you have fun with maths, and impress your friends!

 

Shakuntala Devi’s 84th birthday: Google doodles a calculator for the human computer

Source: http://ibnlive.in.com/news/shakuntala-devis-84th-birthday-google-doodles-a-calculator-for-the-human-computer/432095-11.html

Shakuntala Devi\'s 84th birthday: Google doodles a calculator for the human computer

New Delhi: Google is celebrating the 84th birth anniversary of mathematical genius Shakuntala Devi, nicknamed “human computer” for her ability to make complex mental calculations, with a doodle on its India home page.

The doodle salutes Shakuntala Devi’s amazing calculating abilities with a doodle that resembles a calculator.

Shakuntala Devi found a slot in the Guinness Book of World Record for her outstanding ability and wrote numerous books like ‘Fun with Numbers’, ‘Astrology for You’, ‘Puzzles to Puzzle You’, and ‘Mathablit’. She had the ability to tell the day of the week of any given date in the last century in a jiffy. Coming from a humble family, Shakuntala Devi’s father was a circus performer who did trapeze, tightrope and cannonball shows.

Read more at: http://ibnlive.in.com/news/shakuntala-devis-84th-birthday-google-doodles-a-calculator-for-the-human-computer/432095-11.html

Puzzles to Puzzle You

Mathematician gives evidence at the O.J Simpson trial, helped find diamonds and now is determining the cause of cancer.

Who says Mathematics is useless? It can be useful one day in your career, or just for increasing your general knowledge.

Source: http://www.news.com.au/national/mathematician-professor-terry-speed-wins-pms-science-prize/story-fncynjr2-1226749944856

Mathematician Professor Terry Speed wins PM’s science prize

 

Professor Terry Speed, Head of Bioinformatics at the Walter and Eliza Hall Institute of Medical Research, Melbourne, who has bee

Professor Terry Speed, Head of Bioinformatics at the Walter and Eliza Hall Institute of Medical Research, Melbourne, who has been awarded the Prime Minister’s Award for Science. Picture: Ray Strange Source: News Limited

The man who last night won the Prime Minister’s Science Prize agrees maths is “not sexy” but it saw him give evidence at the O.J Simpson trial, helped find diamonds and now is determining the cause of cancer.

Mathematician Professor Terry Speed was called as an expert witness for O.J. Simpson in the famous 1995 murder trial where he helped explain to the jury how statistics underpinning DNA worked.

Simpson was acquitted after a trial that lasted more than eight months because his lawyers were able to persuade the jurors that there was reasonable doubt about the DNA evidence.

Forty five years ago Professor Speed testified at the trial of Ronald Ryan, the last man to be hanged in Australia.

He had to explain the geometry of the trajectory of bullets in the case.

In an extensive career the 70 year old statistics whiz has helped determine the size and distribution of Argyle diamonds and looked at kangaroo genomics.

Right now he is working at the cutting edge of medical science helping scientists develop statistical tools to understand the huge volumes of information coming from the human genome.

Work he’s done for a company on a thyroid cancer diagnostic test could help prevent thousands of people from having their thyroids removed unnecessarily.

At present some thyroid tests are inconclusive and tumours are removed even though they turn out to be benign leaving the patient taking hormone replacement therapy for the rest of their lives.

Some of his work is in developing tools that find which genes or gene characteristics may cause cancer if they are switched on or off.

Professor Speed says part of the reason so many people don’t want to study maths and science is they don’t see its potential.

He’s spent his life applying mathematical theories to crime, farming, mining and medical science.

Read more at http://www.news.com.au/national/mathematician-professor-terry-speed-wins-pms-science-prize/story-fncynjr2-1226749944856

Maths Skills to be a Doctor

Doctor and Lawyer are the top two favourite careers in Singapore. Do doctors need to use Maths? Read the below to find out.

Even if Maths is not directly needed, the logical thinking skills learnt in Mathematics will definitely be of great use. 🙂

I am not a medical doctor, but my two younger siblings are medical students, and the Mathematical knowledge and thinking skills have definitely helped them in their medical studies.

Source: http://www.rossu.edu/medical-school/students/Mathematics-in-Medicine-.cfm

Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are:

1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc.

2. An understanding of the core statistical concepts most commonly represented in the medical literature.

3. Knowledge of algebra to understand calculations of acid–base status, etc.

4. Ability to appreciate whether or not results are mathematically plausible.    (Nusbaum, 2006)

The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure.

 

Source: http://everydaylife.globalpost.com/kind-math-work-doctor-know-26082.html

It’s often unclear from your interactions with a doctor how much math she is using in order to treat you. While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly.

Dosages and Half-Life

One of the most common ways in which doctors use mathematics is in the determination of medicine prescriptions and dosages. Doctors not only have to use basic arithmetic to calculate what dosage of a particular drug will be effective for your height and body type over a specific period of time, they will also have to be aware of the medicine’s cycle through the body and how the dosage of one drug compares with the dosage of a similar type of drug. Sometimes doctors have to use calculus to figure out the right dosage of a drug. Calculus is the study of how changing variables affect a system. In the human body, the kidney processes medicine. However, people’s kidneys are at varying levels of health. Doctors can designate the kidney as a changing function in a calculus equation known as the Cockroft-Gault equation. This equation uses the level of creatine in a patient’s blood to find the level of the kidney’s functioning, which allows the doctor to determine the appropriate dose.

Cancer Treatment

When a doctor administers radiation therapy to a cancer patient, the radiation beams have to cross each other at specific angles, so that they harm the cancerous tumor without harming the surrounding healthy tissue. The precise numbers for these angles must be calculated mathematically. Cancer tends to respond to any drug by mutating so that its DNA is no longer affected by that drug. Oncologists and medical scientists have decided to target cancerous tumors with many different kinds of drugs at once so that the cancer is unable to respond adequately. They use complex mathematical models that plot the speed and timing of the cancer’s different mutations to figure out what combinations and dosages of different drugs should be used.

Medical Images and Tests

Doctors in medical imaging use two-dimensional images of a patient’s body taken from thousands of angles to create a three-dimensional image for analysis. Determining what angles should be used and how they will fit together requires mathematics. Medical researchers who study disease will analyze the mathematical dimensions of these images. Neurologists who run EEGs on patients to measure their brain waves must add and subtract different voltages and use Fourier transforms to filter out signal static. Fourier transforms are used to alter functions in calculus.

Treatment Research

Medical scientists working with cardiologists use differential equations to describe blood flow dynamics. They also build sophisticated computer models to find the ideal size of an artificial aorta and where to place it in an infant pending a heart transplant. Doctors have to read medical journals to keep up on the latest scientific findings for the benefit of their patients. In addition to describing the calculus used to model health conditions, medical journal studies also make heavy use of statistics and probability to describe the health conditions of whole populations and the likelihood that different treatments will be effective.

New Additional Maths Syllabus (Syllabus 4047) TO BE IMPLEMENTED FROM YEAR OF EXAMINATION 2014

http://www.seab.gov.sg/oLevel/2014Syllabus/4047_2014.pdf

There are some minor changes to the A Maths Syllabus in 2014. Wishing everyone taking the new syllabus all the best!

Main Differences

Topics Added:

– knowledge of a^3+b^3=(a+b)(a^2-ab+b^2) and a^3-b^3=(a-b)(a^2+ab+b^2) is needed

Topics Removed:

– Intersecting chords theorem and tangent-secant theorem for circles removed

– exclude solving simultaneous equations using inverse matrix method

O Level Maths Group Tuition

https://mathtuition88.com/group-tuition/

https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Mathematics homework

E Maths Group Tuition Centre; Clementi Town Secondary School Prelim 2012 Solution

Travel-boat-malta
Travel-boat-malta (Photo credit: Wikipedia)

Q5) The speed of a boat in still water is 60 km/h.

On a particular day, the speed of the current is x km/h.

(a) Find an expression for the speed of the boat

(I) against the current, [1]

Against the current, the boat would travel slower! This is related to the Chinese proverb, 逆水行舟,不进则退, which means “Like a boat sailing against the current, we must forge ahead or be swept downstream.”

Hence, the speed of the boat is 60-x km/h.

(ii) with the current. [1]

60+x km/h

(b) Find an expression for the time required to travel a distance of 80km

(I) against the current,  [1]

Recall that \displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed}}

Hence, the time required is \displaystyle \frac{80}{60-x} h

(ii) with the current. [1]

\displaystyle \frac{80}{60+x} h

(c) If the boat takes 20 minutes longer to travel against the current than it takes to travel with the current, write down an equation in x and show that it can be expressed as x^2+480x-3600=0   [2]

Note: We must change 20 minutes into 1/3 hours!

\frac{80}{60-x}=\frac{1}{3}+\frac{80}{60+x}

There are many ways to proceed from here, one way is to change the Right Hand Side into common denominator, and then cross-multiply.

\displaystyle \frac{80}{60-x}=\frac{60+x}{3(60+x)}+\frac{240}{3(60+x)}=\frac{300+x}{3(60+x)}

Cross-multiply,

240(60+x)=(300+x)(60-x)

14400+240x=18000-300x+60x-x^2

x^2+480x-3600=0 (shown)

(d) Solve this equation, giving your answers correct to 2 decimal places. [2]

Using the quadratic formula,

\displaystyle x=\frac{-480\pm\sqrt{480^2-4(1)(-3600)}}{2}=7.386 \text{ or } -487.386

Answer to 2 d.p. is x=7.39 \text{ or } -487.39

(e) Hence, find the time taken, in hours, by the boat to complete a journey of 500 km against the current. [2]

Now we know that the speed of the current is 7.386 km/h.

Hence, the time taken is \frac{500}{60-7.386}=9.50 h

Maths Group Tuition at Bishan 2014

Maths Group Tuition starting in 2014!

Secondary to JC Classes for Maths Group Tuition starting in 2014!

Location: Block 230 Bishan Street 23 #B1-35 S(570230)

Google Map: http://goo.gl/maps/chjWB

Directions to Bishan Tuition Centre:

A) Via BISHAN MRT (NS17/CC15)

(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.

Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)

It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).

Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary).

Mobius Strip

Ad: Maths Group Tuition 2014

Source: http://www.youtube.com/watch?v=BVsIAa2XNKc

Source: http://en.wikipedia.org/wiki/M%C3%B6bius_strip

The Mobius Strip is a really interesting mathematical surface with just one side. It is easy to make, and cutting it produces many surprising effects! 🙂

The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmbiəs/; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.[1][2][3]

A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. In Euclidean space there are two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. That is to say, it is a chiral object with “handedness” (right-handed or left-handed).

The Möbius band (equally known as the Möbius strip) is not a surface of only one geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the (closed) Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any closed rectangle with length L and width W can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in 3-dimensional space, and others cannot (see section Fattest rectangular Möbius strip in 3-space below). Yet another example is the complete open Möbius band (see section Open Möbius band below). Topologically, this is slightly different from the more usual — closed — Möbius band, in that any open Möbius band has no boundary.

It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.[4]

The Euler characteristic of the Möbius strip is zero.

Understanding the Birthday Paradox

Source: http://betterexplained.com/articles/understanding-the-birthday-paradox/

23 people. In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching.

Put down the calculator and pitchfork, I don’t speak heresy. The birthday paradox is strange, counter-intuitive, and completely true. It’s only a “paradox” because our brains can’t handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we’re involved in (both faulty assumptions, by the way).

Let’s see why the paradox happens and how it works.

Continue reading at http://betterexplained.com/articles/understanding-the-birthday-paradox/