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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 [...]

West Asian numbers – Ancient Mesopotamia

By | 2017-09-16T12:39:12+00:00 September 16th, 2017|Science, West Asia|

Neolithic counting tokens The earliest way of writing down numbers was to carve notches in tally sticks, and this method spread from Africa all over Europe and Asia. But by about 9000 BC, people in West Asia began to use a different method of counting. Instead of tally sticks, people made clay tokens in different shapes. The shapes meant different [...]

Babylonian math problem – West Asian science

By | 2017-09-16T12:10:30+00:00 September 16th, 2017|Science, West Asia|

A real Babylonian math problem on a clay tablet This is a real math problem assigned to Babylonian kids in Iraq about 1900 BC. See if you can do it! Here's the problem: Suppose you have two equilateral triangles, one inside the other. Can you figure out the area of the space between the two triangles? [...]

West Asian mathematics – history of math

By | 2017-09-16T12:05:41+00:00 September 16th, 2017|Science, West Asia|

Sumerian multiplication table (2700 BC) Once people in West Asia figured out how to write down numbers, about 3500 BC, they quickly began to want to use cuneiform to write down other mathematical ideas. The earliest example of this that we have is from about 2700 BC. It shows a multiplication table to help people figure out the area of a space by multiplying width [...]

Before 10,000 BC – World history timeline

By | 2017-09-10T15:46:03+00:00 September 10th, 2017|Africa, History|

Sibidu Cave, South Africa. People lived here from about 77,000 BC until about 38,000 years ago. In the early years of human history, beginning with the earliest humans about two million years ago, every place in the world was in the Stone Age, and all the people in the world got their food by hunting and gathering. For a [...]

Plotinus and the Neoplatonists – Roman philosophy

By | 2017-09-04T11:34:58+00:00 September 4th, 2017|Philosophy, Romans|

Bust of Plotinus (Ostia, ca. 250 AD) Around the time of Jesus, philosophers (and regular people) in West Asia and the Roman Empire started to think a lot about what happened to you after you died. The afterlife was very important to the Christians and the Gnostics. But a little later on, Roman philosophers developed a new idea. They suggested that when [...]

Ancient philosophy: ethics, fate, and science

By | 2017-08-16T15:14:40+00:00 August 16th, 2017|Philosophy|

Weighing the souls of the dead Philosophy means the love of wisdom. But what does that mean? It's hard to separate philosophy from religion. And it's also hard to draw a line between philosophy and science and mathematics. All of these are parts of people's search to make order out of nature. They're a way of [...]

Medieval Islamic mathematics

By | 2017-07-27T11:19:32+00:00 July 27th, 2017|Islam, Math|

Indian numbers About 630 AD, just before the Islamic empire got started, people in West Asia learned from traders or traveling scholars about "Arabic" numbers. This new way of writing numbers really came from India. The Arabic word for numbers, in fact, is hindsah, which means "from India". The new numbers included for the first time a way to write [...]

The Islamic story of wheat on the chessboard

By | 2017-07-25T17:33:16+00:00 July 25th, 2017|Islam, Literature|

Muslims playing chess in Spain About 1260 AD, Ibn Khallikan, a Kurdish historian living in the Abbasid Empire (modern Iraq), wrote an encyclopedia with biographies of many famous men (though no women). One of the biographies includes a story about chess and the meaning of "exponential growth." The story takes place in India, because Ibn Khallikan knew that [...]

Invention of Zero – Indian Mathematics

By | 2017-07-22T06:32:34+00:00 July 22nd, 2017|India, Math|

Counting tokens from Mehrgarh in Late Stone Age India The first known use of numbers in India was in the late Stone Age, about 4000 BC. Around this time, people at Mehrgarh began using the counting tokens that people were already using in West Asia. Soon afterwards, people changed over to writing their numbers down, using pictographs. The Harappans in [...]