The young man knew all the angles.

这名选手了解所有旋转角。

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

我记得我把相机旋转了一个小角固定，看它就停在那里。

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

所以现在我们知道如何描述旋转物体角了。

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

假设你想围绕某个轴旋转某个角。

And those eight-dimensional quasicrystals, when turned to a particular angle, cast down a fourth-dimensional quasicrystal.

那些八维拟晶在旋转到特定角时，会投射出一个四维拟晶。

You can adjust the height, pivot, tilt, or rotate painlessly with a swivel mount on the back.

您可以轻松地通过背部旋转支架无痛调节显示器高、旋转、倾斜或旋转角。

You put another one on top, you twist them by some magic number of degrees, three degrees or something.

你在上面再放一个， 然通过某个神奇角数旋转它们，三或者什么。

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

当腿向推皮带时，这个角旋转数字传递给算法，表示" 我们喜欢这样" 。

According to Yin, exoskeleton robotics support seniors with weaker muscles, enhancing mobility through force compression and release, rotation speed, and angle adjustments.

尹介绍，机器人为肌肉力量较弱老年人提供支持，通过力压缩与释放、旋转速和角调节来增强行动能力。

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.

所以对于一半旋转，角正弦是正，而对于另一半，角正弦是负。

And then this Arduino, which is the brains of the operation, tells the servo motor how much to rotate, which then rotates this heavy pendulum to the left.

然，这个Arduino——整个系统核心——指示伺服电机旋转多少角，伺服电机随即转动这个沉重摆锤向左摆动。

And if we track the phone's position and rotation, we can easily reverse engineer exactly how the stick puppeteer did, rotating mostly from the point where it was held.

如果我们追踪手机位置和旋转角，就能轻松逆向解析出操纵木偶人是如何操作，主要是从握持点进行旋转。

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，但是他们头像一个完整角一样旋转，就像在恐怖电影中一样，就像在驱魔人一样，当她一路转过头。

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，我们已经知道普通平移或线性速是物体位置变化量。同样，旋转速是物体角变化量。

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.

现在假设你有一个三维点，我们用ijk分量来表示它，你想知道绕指定轴旋转指定角这个点新坐标。

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会以相反方向旋转相同角，将其放置在正实轴上，然按相同幅放大5倍，这意味着你会落在数字25上， 这是幅平方。

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.

用旋转轴和旋转角来考虑三维旋转要容易得多 而不是考虑与这个变换相关完整3×3矩阵。