火柴人 VS 数学(Math)｜分析与解释（视情况补翻译）
来自Youtube网友的一些更正：
7：18 它不是抛物线，它只是沿着一个点旋转了180度，这与圆周率弧度相同。
7：51 這不是毫無意義，他確實在試圖畫一個單位圓。单位圆也可以存在于复平面中，这也是 e^（ix） = cos（x）+isin（x） 的部分原因。
10：19 θ是角度，r是半径。r 是 1，所以 theta/r 只是 theta。他只是增加θ并在圆圈中旋转手。
12：09 写无穷大是写极限接近无穷大时的简写。所以这是合法的。
15：26 据我所知，这里的点代表绘图和绘图，因为它如何绘制以前的单位圆。所以他正在推出由点绘制到 e^ipi 的切线图
16：11 我想艾伦在这里想表达的是，他把点和无穷大结合起来。因此，点变得更加强大，并且可以同时启动更多的切线图。
17：07 实际上你可以，但积分是无穷大。它被称为不适当的积分，它也像一个速记，在它接近无穷大时写下极限。
18：16 从0到无穷大的函数下的面积有可能收敛到有限数。
19：48 這個標誌是希臘字母伽瑪。它通常在数学中用于表示阶乘函数的分析延续。所以基本上它是阶乘的，但对于所有实数。
20：28 我不太确定那个公式是什么，但我认为这是拓扑学中的某个公式，e^ipi 正在增加维度或其他东西，并将橙色家伙送回他的世界。
原文：
Some corrections:
7:18 It was not a parabola, It just rotated itself along a point 180 degrees which is the same as pi radians.
7:51 It is not meaningless, he was indeed trying to draw a unit circle. A unit circle can also exist in the complex plane and that's part of the reason why e^(ix) = cos(x)+isin(x).
10:19 Theta is the angle and r is the radius. r is 1 so theta/r is just theta. He was just increasing theta and rotating the hand in the circle.
12:09 Writing infinity is shorthand for writing the limit as it approaches infinity. So it is legal.
15:26 From what I understood, the dot here represents drawing and graphing because of how it drew out the unit circle from before. So he's launching out tangent graphs drew by the dot to e^ipi
16:11 What I think Alan is trying to convey here is he combined the dot with infinity. So the dot becomes more powerful and can launch a lot more tangent graphs at the same time.
17:07 Actually you can but infinity on integrals. It's called an improper integral and it's also like a shorthand to write the limit as it approaches infinity.
18:16 It is possible for the area under a function from 0 to infinity to converge to a finite number.
19:48 That symbol is the greek letter Gamma. It's usually used in math to represent the analytic continuation of the factorial function. So basically it's factorial but for all real numbers.
20:28 I'm not quite sure what that formula is but I think it's some formula in topology and e^ipi is increasing the dimensions or something and sending the orange guy back to his world.
