Math Riddle (Proof that all triangles are equilateral)

Can you spot the subtle mistake in this video?

Very interesting and a good exercise in geometry proving! 🙂


Featured book:

Tutor in a Book’s Geometry

Need help with Geometry? Designed to replicate the services of a skilled private tutor, the new and improved Tutor in a Book’s Geometry is at your service! TIB’s Geometry is an extremely thorough, teen tested and effective geometry tutorial.

TIB’s Geometry includes more than 500 of the right, well-illustrated, carefully worked out and explained proofs and problems. Throughout TIB’s Geometry, there is ongoing, specific guidance as to the most effective solution and test taking strategies. Recurring patterns, which provide solutions to proofs, are pointed out, explained and illustrated using the visual aids that students find so helpful. Also included are dozens of graphic organizers, which help students understand, remember and recognize the connections between concepts.

TIB’s author Jo Greig intended this book to level the playing field between the students who have tutors and those that don’t. As a long time, very successful private mathematics tutor and teacher, Jo Greig knew exactly how best to accomplish this! TIB’s Geometry 294 pages are packed with every explanation, drawing, hint and memory tool possible! Not only does it have examples of the right proofs and problems, it also manages to impart every bit of the enthusiasm that great tutors impart to their private tutoring students. Ms. Greig holds a bachelors’ degree in mathematics. Dr. J. Shiletto, the book’s mathematics editor, holds a Ph.D in mathematics.

 

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.

Source: http://www.channelnewsasia.com/news/singapore/parents-urged-to-consider/898332.html

Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

          Minister for Education Heng Swee Keat (Photo: MOE)

SINGAPORE: Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

Writing on his Facebook page, Mr Heng said it would be good for parents to have an open talk with their children to know what type of secondary school they are interested in.

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.

So he encourages parents to carefully consider the kind of environment that will best motivate their children, and enable them to develop themselves fully in the next four to five years.

Some children, he said, are late developers and the right environment helps them thrive.

Mr Heng urged parents to think of how best they can help their children develop confidence and enjoy the space to discover his talents and passions.

Continue reading at http://www.channelnewsasia.com/news/singapore/parents-urged-to-consider/898332.html

Time needed for each O Level E Maths / A Maths Question

E Maths / A Maths: Maximum time per question

Paper 1: 2 hours (120 min) — 80 marks

Max. Time taken per mark: 1.5 min per mark

Paper 2: 2 hours 30 minutes (150 min) — 100 marks

Max. Time taken per mark: 1.5 min per mark

In O Levels Maths, speed and accuracy is very important indeed!

Maths Movie to look out for: Hollywood primed for film on Indian math genius Ramanujan

Look out for this movie on Indian math genius Ramanujan starring Dev Patel from “Slumdog Millionaire”!

Ramanujan was a self-taught maths genius from India who had little to no formal education. Yet he was able to come out with stunning formulas such as this approximation for Pi:

\displaystyle\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}

Source: http://in.reuters.com/article/2013/07/25/ramanujan-mathematician-dev-patel-hollyw-idINDEE96O08H20130725

Actor Dev Patel arrives for the season 2 premiere of his HBO drama series ''The Newsroom'' in Hollywood July 10, 2013. REUTERS/Fred Prouser

(Reuters) – A new Hollywood film starring Dev Patel as Srinivasa Ramanujan will put the spotlight on the Indian math genius best known for his work on the theory of prime numbers.

Ramanujan, who died in 1920, was considered one of the brightest minds in mathematics, despite his lack of a formal education.

Patel, who caught Hollywood’s eye in 2008’s Oscar-winning film “Slumdog Millionaire”, has been cast as the lead. Filming begins in September with a British actor playing G.H. Hardy, the mathematician who recognized Ramanujan’s talent and brought him to England in 1914.

“The subject matter of Ramanujan is an Indian story but it is the story of the relationship of India and the West,” the film’s co-producer Edward Pressman told Reuters over the phone.

Continue reading at http://in.reuters.com/article/2013/07/25/ramanujan-mathematician-dev-patel-hollyw-idINDEE96O08H20130725

The Most Famous Tutor – Aristotle

A tutor is an instructor who gives private lessons. The most famous example of a tutor is Aristotle, who tutored Alexander the Great.

Aristotle Altemps Inv8575.jpg
Aristotle

Source: http://en.wikipedia.org/wiki/Aristotle

Aristotle (Ancient Greek: Ἀριστοτέλης [aristotélɛːs], Aristotélēs) (384 BC – 322 BC)[1] was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. Together with Plato and Socrates (Plato’s teacher), Aristotle is one of the most important founding figures in Western philosophy. Aristotle’s writings were the first to create a comprehensive system of Western philosophy, encompassing ethics, aesthetics, logic, science, politics, and metaphysics.

BattleofIssus333BC-mosaic-detail1.jpg
Alexander the Great

Source: http://en.wikipedia.org/wiki/Alexander_the_Great

Alexander III of Macedon (20/21 July 356 – 10/11 June 323 BC), commonly known as Alexander the Great (Greek: Ἀλέξανδρος ὁ Μέγας, Aléxandros ho Mégasiii[›] from the Greek ἀλέξω alexo “to defend, help” + ἀνήρ aner “man”), was a king of Macedon, a state in northern ancient Greece. Born in Pella in 356 BC, Alexander was tutored by Aristotle until the age of 16. By the age of thirty, he had created one of the largest empires of the ancient world, stretching from the Ionian Sea to the Himalayas.[1] He was undefeated in battle and is considered one of history’s most successful commanders.[2]

Featured Mathematician of the Day: Shing-Tung Yau

Maths Group Tuition starting in 2014!

Source: http://en.wikipedia.org/wiki/Shing-Tung_Yau

Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng; born April 4, 1949) is a Chinese-born American mathematician. He won the Fields Medal in 1982.

Yau’s work is mainly in differential geometry, especially in geometric analysis. His contributions have had an influence on both physics and mathematics and he has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein‘s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi–Yau compactification—to show that string theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today.

Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died.

After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to the University of California, Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University.

Since 1987, he has been at Harvard University,[1] where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.

Shing-Tung Yau at Harvard Law School dining hall
Shing-Tung Yau at Harvard Law School dining hall (Photo credit: Wikipedia)

NUS Top in Asia according to latest QS World University Rankings by Subject

Source: http://newshub.nus.edu.sg/headlines/1305/qs_08May13.php

Top in Asia according to latest QS World University Rankings by Subject

08 May 2013

NUS is the best-performing university in Asia in the 2013 QS World University Rankings by Subject. With 12 subjects ranked top 10, NUS has secured the 8th position among universities globally in this subject ranking.
On the results, NUS Deputy President (Academic Affairs) and Provost Professor Tan Eng Chye said: “This is a strong international recognition of NUS’ strengths in humanities and languages, engineering and technology, sciences, medicine and social sciences.”
Prof Tan noted that the rankings served as an acknowledgement of the exceptional work carried out by faculty and staff in education and research.
NUS fared well, ranking among the world’s top 10 universities for 12 subjects namely Statistics, Mathematics, Material Sciences, Pharmacy & Pharmacology, Communication & Media Studies, Geography, Politics & International Studies, Modern Languages, Computer Science & Information Systems and Engineering (mechanical, aeronautical, manufacturing, electrical & electronic, chemical).

Continue reading at: http://newshub.nus.edu.sg/headlines/1305/qs_08May13.php

Japanese Math Professor Excellent Optical Illusionist

Source: http://www.youtube.com/watch?v=Wx4yi5m8IfI

Uploaded on Mar  8, 2011

Japanese mathematics professor Kokichi Sugihara spends much of his time in a world where up is down and three dimensions are really only two. Professor Sugihara is one of the world’s leading exponents of optical illusion, a mathematical art-form that he says could have application in the real world.
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Three sloped ramps are aligned along three of the four sides of a square. Each ramp appears to be sloped in the same direction but when a marble is placed at one end of the ramp it seems to defy gravity.
It’s called an “anti-gravity slide”. Only when the the entire structure is turned 180 degrees, is the illusion revealed.
Japanese mathematics professor Kokichi Sugihara from the Meiji Institute near Tokyo, has made a career of creating optical illusions. He’s devised and built more than a hundred of them, like this one called “Perches and a Ring”.
[Kokichi Sugihara, Meiji University Professor]: “Among these models, there are those which are reproductions of optical illusions, and others that seem like normal models, but when you add movement to them, they show movement that should be impossible in real life. This is done by using the same trick, and I call them ‘impossible motions’.”
Professor Sugihara’s “impossible motions” have been recognized around the world. He won first prize in an international competition last year with this one, called “Magnet-Like Slopes”.
Sugihara says the success of his illusions is tied to human perception. Because humans have the capacity to perceive two-dimensional objects as being three-dimensional, they can be fooled into believing that something “impossible” is taking place during the course of the illusion.
For Sugiraha the illusions aren’t just for amusement. He says they have real world application. For example, he says misjudgments made by drivers on steeply curved roads could be mitigated by changing their perceptions of the immediate environment.
[Kokichi Sugihara, Meiji University Professor]: “If we can find how drivers misjudge an incline, we would be able to construct roads where these incidents are less likely to happen. In other cases, we could also reorganize the surrounding environment so that drivers could more easily see the difference between an ascending and descending road, and it could lead to reducing traffic jams.”
Sugihara says says his dream is to create playground amusements – even buildings with his models. More immediately though he has plans for an “impossible object exhibition”, a venue to demonstrate that seeing really is believing.

Carl Friedrich Gauss

Source: http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

Johann Carl Friedrich Gauss (/ɡs/; German: Gauß, pronounced [ɡaʊs] ( listen); Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.

Sometimes referred to as the Princeps mathematicorum[1] (Latin, “the Prince of Mathematicians” or “the foremost of mathematicians”) and “greatest mathematician since antiquity“, Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.[2]

Carl Friedrich Gauss.jpg

Continue reading at http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

Student Advice: Comments on Perseverance

Source: http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

Comments on Perseverance:

One source of confusion for students when they reach college and begin to  do college-level mathematics is this:  in high school, it is usually pretty  apparent what formula or technique needs to be applied, as much of the  material in high school is computational or procedural.  In college,  however, mathematics becomes more conceptual, and it is much harder to  know what to do when you first start a problem.  As a consequence of this,  many students give up on a problem too early.

If you don’t immediately know how to attack a problem, this doesn’t mean you  are stupid,


If you already know how to do it, it’s not  really a problem.

or that you don’t understand what’s going on; that’s just how  real problems work.  After all, if you already know how to do it, it’s not  really a problem, is it?  You should expect to be confused at first.   There’s no way you can know ahead of time how to solve every problem that  you will face in life.  You’re only hope, and therefore your goal as a  student, is to get experience with working through hard problems on your  own.  That way, you will continue to be able to do so once you leave  college.

One of the first steps in this is to realize that not knowing how, and the  frustration that accompanies that, is part of the process.  Then you have  to start to figure out the questions that you can ask to help you to break  down the problem, so that you can figure out how it really works.  What’s  really important in it?  What is the central concept?  What roles do the  definitions play?  How is this related to other things I know?

Continue reading at http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

Famous Nonmathematicians who studied Mathematics

This is a list of Famous Nonmathematicians who studied Mathematics, featuring Singapore’s Prime Minister, Lee Hsien Loong, with first class honours in mathematics from Trinity College, University of Cambridge.

Source: http://www.math.uh.edu/~tomforde/famous.html

We often tell our students that there are many things besides teaching and actuarial work that they can do with a degree in mathematics, but they often don’t believe us. Here is a list of well-known people who were math majors (or some equivalent in other countries and times), although not all of them completed their degrees.

THE PUBLIC REALM
•Ralph Abernathy, civil rights leader and Martin Luther King’s closest aide.

•Corazon Aquino, former President of the Philippines. She was a math minor at the College of Mt. St. Vincent.

•Harry Blackmun, Associate Justice of the US Supreme Court, AB summa cum laude in mathematics at Harvard.

•Simeon DeWitt, was the first math major at Rutgers. He became General George Washington’s Chief Geographer in the Revolutionary War. His maps of Yorktown helped win the final battle of that war. Afterwards (1784-1834) he was the Surveyor General for New York State; he helped to plan the Erie Canal, and to develop the grid system of streets and avenues in New York City, among other things.

•David Dinkins, Mayor of New York, BA in mathematics from Howard.

•Alberto Fujimori, President of Peru, MS in mathematics from the University of Wisconsin-Milwaukee.

•Ira Glasser, Executive Director of the American Civil Liberties Union, both a BS and an MA.

•Lee Hsien Loong, Deputy Prime Minister of Singapore, a Bachelor’s from Cambridge.

Read more at http://www.math.uh.edu/~tomforde/famous.html

学好数理化,走遍天下都不怕。

Study mathematics, physics, and chemistry well. Then no matter where you go, you will fear nothing!

Ancient Chinese Proverb

Source: http://www.liuxue86.com/a/1133118.html

美国留学打工 “学好数理化,走遍天下都不怕。”在美国一样适用

美国人口普查局的最新报告显示:同样是学士学位,按工作40年计算,工程专业的毕业生比教育学的毕业生多赚160万美元。真可谓是“男怕入错行,女怕嫁错郎。”

根据美国人口普查局最新发布的2011年社区调查报告,美国具有学士学位的大学毕业证全职工作的人每年中位薪资收入是64396美元,这些人既包括新毕业的大学生,也包括那也干的一辈子最高学位是学士的全职工作者。其中工程专业的薪资最高,平均每年高达91611美元,电脑与数学专业排第二位,年均80180美元,物理、化学、医学等自然科学专业薪水也不错,以80037美元排第三位。在另一个极端视觉和表演艺术专业薪水最低,平均一年只有50484美元,教育专业只有50902美元,心理学专业为55509美元,列倒数前三名,由此可以推算出来从事工程专业工作的人平均每年比从事表演艺术专业的人多挣4万美元,以一个人工作40年计算整个职业生涯收入平均相差160万美元,差距还是很惊人的。

Mathematics and 3D printing

Source: http://samuelcavazos.com/2013/07/12/mathematics-and-3d-printing/

Nice post on Mathematics and 3D printing!

3D printing is the latest advance in technology, that will possibly revolutionise the world!

Quote from source:

Below are some images of some of the mathematical structures he and Carlos Salinas have done using a MakerBot 3D printer. Most of these were first designed by using a software called Mathematica, which has the ability to handle complex surfaces and then create the file necessary to run on the MakerBot Software.

http://samuelcavazos.com/2013/07/12/mathematics-and-3d-printing/

 

The Key To Career Success

Source: http://www.huffingtonpost.com/brooks-mccorcle/the-key-to-career-success_b_3511254.html

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” ~ Stan Gudder, Mathematician

Math, at its core, is about solving problems — about breaking a challenge into its basic elements to be investigated, tested, manipulated and understood. Math can give you the tools to find a winning formula. And, it can create the path to your career.

Math is the key to unlocking possibilities. It frees you up to think creatively about solutions and to focus your attention on what truly matters at the end of the day.

Finally, math empowers you to be a better leader and to remain open to new ideas. It sparks creativity and learning. It gives you confidence and conviction to say “YES!” when you’re asked to take on a new challenge. It helps you attract and energize the people you hire to help you.  In a marketplace that’s moving so fast, it’s important to constantly listen, learn, analyze and formulate new ways to serve customers.  Math provides the foundation for doing just that.

Want to succeed? It’s simple … math.

EDUC115N: How to Learn Math (Stanford Online Maths Education Course )

I will be attending this exciting online course by Stanford on Math Education. Do feel free to join it too, it is suitable for teachers and other helpers of math learners, such as parents.

stanford-maths-tuition

EDUC115N: How to Learn Math 

(Source: https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about)

About This Course

In July 2013 a new course will be available on Stanford’s free on-line platform. The course is a short intervention designed to change students’ relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.

Concepts

1. Knocking down the myths about math.        Math is not about speed, memorization or learning lots of rules. There is no such  thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.

2. Math and Mindset.         Participants will be encouraged to develop a growth mindset, they will see evidence of  how mindset changes students’ learning trajectories, and learn how it can be  developed.

3. Mistakes, Challenges & Persistence.        What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.

4. Teaching Math for a Growth Mindset.      This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.

5. Conceptual Learning. Part I. Number Sense.        Math is a conceptual subject– we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.

6. Conceptual Learning. Part II. Connections, Representations, Questions.        In this session we will look at and solve math problems at many different  grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (film maker, inventor of self-driving cars etc) will show the importance of conceptual math.

7. Appreciating Algebra.        Participants will learn some key research findings in the teaching and learning of algebra and learn about a case of algebra teaching.

8. Going From This Course to a New Mathematical Future.        This session will review the ideas of the course and think about the way towards a new mathematical future.

Make Britain Count: ‘Stop telling children maths isn’t for them’

Source: http://www.telegraph.co.uk/education/maths-reform/9621100/Make-Britain-Count-Stop-telling-children-maths-isnt-for-them.html

“The title comes from the central argument of the book,” says Birmingham-raised
Boaler, “namely the idea that maths is a gift that some have and some don’t.
That’s the elephant in the classroom. And I want to banish it. I believe
passionately that everybody can be good at maths. But you don’t have to take my word for it. Studies of the brain show that all kids can do well at maths,
unless they have some specific learning difficulty.”

But what about those booming Asian economies, with their ready flow of mathematically able graduates? “There are a lot of misconceptions about the methods that are used in China, Japan and Korea,” replies Boaler. “Their way of teaching maths is much more conceptual than it is in England. If you look at the textbooks they use, they are tiny.”

Professor Boaler’s tips on how parents can help Make Britain Count.

1 Encourage children to play maths puzzles and games at home. Anything with a dice will help them enjoy maths and develop numeracy and logic skills.

2 Never tell children they are wrong when they are working on maths problems. There is always some logic to what they are doing. So if your child multiplies three by four and gets seven, try: “Oh I see what you are thinking, you are using what you know about addition to add three and four. When we multiply we have four groups of three…”

3 Maths is not about speed. In younger years, forcing kids to work fast on maths is the best way to start maths anxiety, especially among girls.

4 Don’t tell your children you were bad at maths at school. Or that you disliked it. This is especially important if you are a mother.

5 Encourage number sense. What separates high and low achievers in primary school is number sense.

6 Encourage a “growth mindset” – the idea that ability changes as you work more and learn more.

Mathematics is an art

Taken from http://www.maa.org/devlin/lockhartslament.pdf

The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians? Part of the problem is that nobody has the faintest idea what it is that mathematicians do. The common perception seems to be that mathematicians are somehow connected with science— perhaps they help the scientists with their formulas, or feed big numbers into computers for some reason or other. There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category. Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood. So let me try to explain what mathematics is, and what mathematicians do. I can hardly do better than to begin with G.H. Hardy’s excellent description: A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

.

成语数学

An alternative answer to Q1) 20 除 3 is “陆续不断”.

20除以3,因为它的答案接近于6.6666,所以这道题的答案是陆续不断,或者是六六大顺都行,百分之一就是百里挑一,9寸加1寸等于一尺即是得寸进尺,12345609,七零八落,1、3、5、7、9无双数所以叫做举世无双,或者你把它答出天下无双都行,如此小升初的难题您答对了吗?

Source: http://politics.people.com.cn/n/2013/0528/c70731-21638931.html

Math Online Tom Circle

中国的小学离校考试 (PSLE) 「神题」: 猜成语
1) 20 除 3
2)1 除100
3)9寸+1寸=1尺
4)12345609
5)1,3,5,7,9

答案::
1) 20/3= 6.666 六六大顺
2)百中挑一
3)得寸進尺
4)七零八落
5)举世无双

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