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

几何中最著名关系是直三边和斜边之间关系。

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

取四个全等直三，边分别长 a 和 b，斜边长 c。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是边长 1 直三之斜边。

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 直三斜边。

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

这表明直三各边平方加起来等于其斜边平方。

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.

了考虑投影， 让我们制作一个像这样小直三，其中球面矩高是斜边，它投影是其中一条腿。

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）做出了精彩证明；这个定理是说，对于一个直三，一边平方加上另一边平方等于斜边平方。

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.

他们都著名毕达哥拉斯定理提出了优雅证明，这条规则说对于直三，一侧平方加上另一侧平方等于斜边平方。