Pythagorean Triples Were Known 1,000 Years Before Pythagoras

The Babylonian clay tablet from the collection of Columbia University dating from 1,000 years before Pythagoras’s theorem is a trigonometric table which has 15 pairs of numbers forming Pythagorean triples: three whole numbers a, b and c:

a2 + b2 = c2

The tabet is known as the world’s oldest trig table. Babylonians used the base-60 numbers, which permitted many more accurate fractions than the contemporary base 10. For example, 2/3 = 0.6666… (or 40 minutes) was a finite number. The base-60 system were inspired from such shapes as a circle and the regular hexagon (see an example).

Advertisements

2015 OECD PISA Global Education Survey

The top OECD countries were Singapore, Japan, Estonia, Finland and Canada. These countries also achieve high levels of performance and equity in education outcomes.

pisa2015-math

Source: OCDE

More than one in four students in Beijing-Shanghai-Jiangsu-Guangdong (China), Hong Kong (China), Singapore and Chinese Taipei are top-performing students in mathematics, a higher share than anywhere else.

Students in larger schools score higher in science and are more likely than students in smaller schools. Students in smaller schools reported a better disciplinary climate.

Gender gap: the share of top performers in science is larger among boys than among girls. Finland is the only country in which girls are more likely to be top performers than boys. Girls mostly seek positions in the health sector and boys  in becoming ICT professionals, scientists or engineers.

Five sample PISA Math questions:

  1. Cycling
  2. Numbers
  3. Many years ago
  4. Australia, Germany, and USA
  5. Math test score

 

Classics of Recreational Math

The classical recreational math authors are Lewis Carroll,  Henry DudleyMartin GardnerSam Loyd, and Yakov Perelman.

This an example of classical math puzzles: http://www.aplusclick.com/k/5423.htm :

(102 + 112 + 122) – (132 + 142) = ?

The picture “Mental Count” of Russian painter Nikolay Bogdanov-Belsky contains the simple calculation. Image source : Wikipedia

427px-BogdanovBelsky_UstnySchet

 

Dream Math

Everybody dreams.

rsauter-boyThe boy dreams of being an astronaut.

How long does he need to study and work until his dream can become reality?

Answer

 

Which job does not require math?

 

The photograph courtesy of Roland Sauter

 

Extraordinary Math Teaching by Dan Finkel

Dan Finkel suggested principles of extraordinary math teaching:

Math can the best of time or the worst of time.

 

 

1) Start with a question.

2) Thinking happens only when you have time to struggle.

3) (Teacher), you are not the answer key.

4) Say yes to your students’ ideas.

5) Play!

A marvelous quotation is attributed to the most brilliant scientist of the modern age, Albert Einstein: “Play is the highest form of research.”

 

 

 

Project Starters

Challenging puzzlers to create a positive attitude to real projects.

Estimate or Calculate?

” in the real world, we constantly settle for estimates, whereas mathematics — see the SAT — demands that you get the answer precisely right.” – Andrew Hacker in The New York Times article “The Wrong Way We Teach Math

 

boy sitting on money, money concept

Estimate or Calculate?

My answer is one of them and do it fast.