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

取四个全等的直角三角形，两边分别长 a 和 b，斜边长 c。

Root 2 simply is the hypotenuse of a right triangle

√2 两边长度为 1 的 直角三角形之斜边。

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

几何中著名的关系直角三角形的边和斜边之间的关系。

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 直角三角形的斜边。

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

这表明直角三角形各边的平方加起来等于其斜边的平方。

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.

为了考虑投影， 让我们制作一个像这样的小直角三角形，其中球面矩形的高度斜边，它的投影其中一条腿。

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）做出了精彩的证明；这个定理说，对于一个直角三角形，一边的平方加上另一边的平方等于斜边的平方。

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.

他们都为著名的毕达哥拉斯定理提出了优雅的证明，这条规则说对于直角三角形，一侧的平方加上另一侧的平方等于斜边的平方。