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).

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Why Is X The Unknown?

Terry Moore explains that the inventors of algebra were Arabic scientists. Their definition:

X = something, some undefined unknown thing = the unknown thing.

When the books were translated from Arabic to Spanish the Arabic unknown was “SH” that did not exist inSpanish. They replaced it by “X“.  It migrated to other European languages 600 years ago.

X is “X” because Spanish language does not have “SH“.

Cat, Rat, Hat, and Mat

 

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Mary has a cat, and a rat, and a hat, and a mat.

If the cat is on the mat, and rat is in the hat, but the hat is on the mat, where is the rat?

This is a simple puzzle asked by Leslie Green, who collects dozens challenging puzzles.  The collection of Leslie Logic and Math Puzzles is presented at the website Aplusclick. It’s worth to try the challenging questions.

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Selfie Math

Jim is going on a tour around the world. He has 5 tops, 4 bottoms, and 3 pairs of footwear. He wants to post a selfie everyday to show different places and his different outfits to his girl-friend Mary, who stays at home. He does not want to wear the same outfit twice. ## For how many days does he have enough clothing?

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Leslie Green gives the answer : 96 days.

Can you explain why it is 96? What is logic behind?

 

 

Guesstimate Methods

Guesstimate is an estimate based on a mixture of guesswork and calculation.

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“Everything should be made as simple as possible, but not simpler.” – Albert Einstein

“The purpose of computing is insight, not numbers.” – Richard Hamming

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.

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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