# The Theorem in Ancient China

Another civilization that had knowledge of the Pythagorean identity was the Chinese civilization. A Chinese astronomical and mathematical treatise known as Chou Pei Suan Ching (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) suggest that the Chinese also knew of the Pythagorean Theorem, quite possibly before the Greeks did. What is fascinating about this is that the Chinese and Greek cultures developed in isolation from each other, meaning that the Greek and Chinese developments were unlikely influenced by each other. (Tian-Se pp. 253-266) The treatise is thought to have been written around 600 BC, just before the time of Pythagoras. Within the text, there are diagrams that suggest that the Chinese Civilization was aware of the Pythagorean theorem, and what sets them apart from the Babylonians, is that they were able to prove it. The proof given was a geometric proof very similar to the proof that Euclid provided in his book, Euclid’s Elements. (Burton 108)

Much like the Greeks, the Chinese took 4 right triangles and arranged them so that the hypotenuse of each triangle became the side of a square. By rearranging these figures they came up with two representations are were able to solve them for the identity that we know today. However, the words “Behold!,” were written as the proof rather than the algebra that we use today.

There is debate as to when this relationship was found exactly, but one thing is sure. They Chinese not only knew the Pythagorean Theorem, but also knew how to use it. In the treatise, it explains how to use the theorem to find the depth of pools, or more practically, rivers and streams. This application influenced Indian mathematicians that these applications started to arise in their writing later on.

Further, mathematicians in ancient China were able to use this identity to find the distance to astronomical objects. By using the shadows cast by the sun and angle measurements, they were able to calculate the distance to the sun. (Tian-Se pp. 260-264)

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