Take four identical right triangles with side lengths a and b and hypotenuse length c.

取四个全等的直三形，两分别长 a 和 b，长 c。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是两长度为 1 的 直三形之。

The most famous relation in geometry is the relation between the sides and the hypotenuse of a right triangle.

几何中最著名的关系是直三形的和之间的关系。

When you draw a vector, it's a lot like the HYPOTENUSE of a right angle triangle.

当你画一个箭头时，它很像 直三形的。

That states that the squares of the sides of a right triangle add up to the square of its hypotenuse.

这表明直三形各的平方加起来等于其的平方。

To think about the projection, let's make a little right triangle like this, where what was the height of our spherical rectangle is the hypotenuse, and its projection is one of the legs.

要想考虑投影， 我们可以画一个小直三形，其中球面矩形的高度是，其投影是其中一个直。

They all came up with elegant proofs for the famous Pythagorean theorem; the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都对毕达哥拉斯定理（勾股定理）做出了精彩的证明；这个定理是说，对于一个直三形，一的平方加上另一的平方等于的平方。

And so what they thought, and this is what the ancient historians described, is that they effectively tried to draw a right angle triangle with the two entrances at each end of the hypotenuse.

他们认为， 古代历史学家描述的就是，他们实际上试图画一个直三形， 两个入口分别位于的两端。

They all came up with elegant proofs for the famous Pythagorean theorem, the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都为着名的勾股定理提出了简洁的证明，该定理指出， 对于一个直三形，一条直的平方加上另一条直的平方等于的平方。