# The origin of 勾 and 股 in The Pythagorean Theorem 勾股定理

The Chinese name for the Pythagorean Theorem is 勾股定理

Take a right angle triangle ABC

Let side AB be the shortest side.

Let AC be the second shortest side.

BC is therefore the longest side and the hypotenuse.

In Chinese the side AB is called 勾, the side AC is called 股 and the side BC is called 弦.

In English the two shorter sides are called “legs”.

Why were the two “legs” called 勾 and 股 ?

It makes sense that the hypotenuse is called 弦 as the triangle is usually drawn such that the hypotenuse is diagonal.

• You can read the Chinese version of Wikipedia and the History section in the English version. – young99 Dec 25 '19 at 11:20
• @young99 Thanks , but the English version doesn’t mention 勾 or 股 and I can’t find the answer in the Chinese version. If you find it please let me know. – Kantura Dec 25 '19 at 13:04

in ancient china, the right angle triangle is named "勾股形".

the 國語辭典 has this entry: 勾股, explained as

the short side near the right angle is called "勾", the longer side near the right angle is called "股"; and the side opposite the right angle is called "弦".

people used something like "勾股", "勾股之法" to describe the equation a²+b²=c²; nowadays, a hybrid naming is used "勾股" (the ancient chinese name) + "定理" (translation of theorem).

btw, the character 句 (u+53e5) and 勾 (u+52fe) mutually borrowed in ancient time.

• Thanks , but that doesn’t answer my question. I already knew all that. My question is why 勾 and 股 ? – Kantura Dec 25 '19 at 12:59
• 勾 = hook, 股 = ply, 弦 = string. May be ancient people just used words for sharps similar to the triangle parts to referring them. 短邊稱為「勾」( Short side is called a hook shape), 長邊稱為「股」(long side is called a ply board shape) – Tang Ho Dec 25 '19 at 14:24
• Imagine a right angle triangle, now the long side is a ply board one the bottom, the short side stands 90 degree on the board would look like a hook extended from the board, and imagine the line connecting the end of the hook and the end of the board as a string – Tang Ho Dec 25 '19 at 14:35
• @tangho, yeah, quite appealing :) – 水巷孑蠻 Dec 25 '19 at 15:05