The young man knew all the angles.

这名选手了解所有的角度。

Let's say you want to rotate some angle around some axis.

假设您想绕个轴个角度。

So now we know how to describe the angle of something that’s rotating.

所以现我们知道如何描述物体的角度了。

I remember just spinning a camera a little and letting it go and watch it stay right there.

我记得我把相机了一个小角度之后固定，看它就停那里。

When the leg pushes the belt backwards, this rotation in angles is a number that is given to the algorithm saying, we like that.

当腿向后推皮带时，这个角度的数字传递给算法，表示" 我们喜欢这样" 。

So for half of the rotation, the sine of the angle is positive, and for the other half, the sine of the angle is negative.

所以对于一半的，角度的的，而对于另一半，角度的负的。

And they're still walking forwards, but their head has rotated in like a complete angle, a bit like in a horror movie, like in The Exorcist, when she turns her head all the way around.

而且他们仍然向前走，但他们的头像一个完整的角度一样，就像恐怖电影中一样，就像驱魔人一样，当她一路过头。

Well, we’ve already learned that plain old translational, or linear, velocity is a measure of an object’s change in position. And in the same way, rotational velocity is a measure of an object’s change in angle.

好吧，我们已经知道普通的平移或线性速度物体位置变化的量度。同样，速度物体角度变化的量度。

And it's much easier to think about a three D rotation in terms of some axis of rotation and an angle by which it's rotating, rather than thinking about the full three by three matrix associated with that transformation.

用轴和角度来考虑三维要容易得多 而不考虑与这个变换相关的完整的3×3矩阵。

Now let's say you have some 3d point, which we'll write with ijk, components, and you want to know the coordinates of what you'll get by rotating this point by your specified angle around your specified axis.

现假设您有一些 3d 点，我们将用 ijk、组件来编写它，并且您想知道通过围绕指定轴该点指定的角度所得到的坐标。

Multiplying by 3-4i rotates by that same angle in the opposite direction, putting it on the positive real axis, then stretches by that same magnitude, 5, meaning you land on the number 25, the square of the magnitude.

乘以 3-4i 会沿相反方向相同的角度，将其放实轴上，然后拉伸相同的大小 5，这意味着您得到数字 25， 即大小的平方。