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Pythagorean Theorem proof

By | 2017-09-25T10:25:04+00:00 September 25th, 2017|Greeks, Math|

A right triangle. This is the proof of the Pythagorean Theorem supposedly written by Pythagoras about 500 BC: The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2. Try it yourself: if Side [...]

Logic and the scientific method

By | 2017-09-06T17:22:05+00:00 September 6th, 2017|Science|

An eclipse of the moon. You can see the curved shadow of the Earth. Once people have seen that something happens through observation, sooner or later it will occur to them to ask why it happens. And is there any way to prove that it will happen the same way every time? Sumerians developed advanced math to [...]

Ancient and medieval science

By | 2017-09-06T12:57:09+00:00 September 6th, 2017|History, Science|

Chinese star chart possibly dating from the 600s AD, during the T'ang Dynasty Science means "knowing" in Latin. It is the process of learning things about the world. People have always wanted to learn more about their world, and they have tried a lot of different ways to find things out. Some of the ways they tried [...]

Proof for the area of a circle

By | 2017-07-28T08:41:36+00:00 July 28th, 2017|Math|

Divide a circle up into sections like an orange We know it's true that A=πr-squared is the area of a circle, but how can we prove that it is always true for every possible circle? Here's how Euclid did it. Start by dividing a circle into sixteen sections like an orange. We know that together they add up to the [...]

Jainism – religion in medieval India

By | 2017-07-21T09:23:04+00:00 July 21st, 2017|India, Religion|

A Jain statue, possibly Mahavira, from about 1200 AD Nobody knows when people first began to follow Jain ideas. Some Jain traditions take their history back to about 2000 BC, in the Harappan period. The first definite evidence of Jain faith, though, comes from about 650 BC, with the Jain leader Parshvanatha. We don't know much for [...]

Who was Pythagoras? Greek Mathematics

By | 2017-07-18T15:30:55+00:00 July 18th, 2017|Greeks, Math|

Doric temple at Paestum, Italy Pythagoras lived in the 500s BC. He was one of the first Greek mathematical thinkers that we know about, after Thales. He spent most of his life in the Greek colonies in Sicily and southern Italy. Pythagoras had a group of followers (like Taoists followed Lao Tzu, or Buddhists followed the Buddha). His followers learned from him and [...]

Greek mathematics – Geometry and Proofs

By | 2017-07-18T11:36:00+00:00 July 18th, 2017|Greeks, Math|

An Egyptian papyrus from about 100 AD which is a piece of one of Euclid's books Because people in ancient Greece had only very clumsy ways of writing down numbers, they didn't like algebra. They found it very hard to write down equations or number problems. Instead, Greek mathematicians were more focused on geometry, and used geometric [...]

Who was Euclid? History of Geometry

By | 2017-07-18T11:26:44+00:00 July 18th, 2017|Africa, Egypt, Science|

An Egyptian papyrus from about 100 AD which is a piece of one of Euclid's books Nobody knows much about Euclid's life anymore - it is all forgotten. We only know that he worked at the University of Alexandria, in Egypt, for a while. There are no pictures of him. We can't even be sure [...]

How to prove the Pythagorean Theorem

By | 2017-10-14T16:39:50+00:00 July 18th, 2017|Greeks, Science|

Diagram for proving the Pythagorean Theorem You can prove the Pythagorean Theorem for yourself, using the proof described on the Pythagorean Theorem page. Just get a square piece of paper, and draw the lines on it that you see in the third drawing (the drawing of a square). Draw the diagonal lines as in [...]

Who was Archimedes? Eureka!

By | 2017-07-18T07:38:57+00:00 July 18th, 2017|History|

Syracuse, Sicily, with Mount Etna in the background Archimedes was born about 287 BC, so he was a little younger than Euclid. Archimedes' father was an astronomer. Because Archimedes was related to the tyrant who ruled Syracuse, on the island of Sicily, he lived his whole life in Sicily, except when he went to study at the University of [...]