來自Youtube網(wǎng)友的一些更正：

7：18 它不是拋物線，它只是沿著一個(gè)點(diǎn)旋轉(zhuǎn)了180度，這與圓周率弧度相同。

7：51 這不是毫無意義，他確實(shí)在試圖畫一個(gè)單位圓。單位圓也可以存在于復(fù)平面中，這也是 e^（ix） = cos（x）+isin（x） 的部分原因。

10：19 θ是角度，r是半徑。r 是 1，所以 theta/r 只是 theta。他只是增加θ并在圓圈中旋轉(zhuǎn)手。

12：09 寫無窮大是寫極限接近無窮大時(shí)的簡(jiǎn)寫。所以這是合法的。

15：26 據(jù)我所知，這里的點(diǎn)代表繪圖和繪圖，因?yàn)樗绾卫L制以前的單位圓。所以他正在推出由點(diǎn)繪制到 e^ipi 的切線圖

16：11 我想艾倫在這里想表達(dá)的是，他把點(diǎn)和無窮大結(jié)合起來。因此，點(diǎn)變得更加強(qiáng)大，并且可以同時(shí)啟動(dòng)更多的切線圖。

17：07 實(shí)際上你可以，但積分是無窮大。它被稱為不適當(dāng)?shù)姆e分，它也像一個(gè)速記，在它接近無窮大時(shí)寫下極限。

18：16 從0到無窮大的函數(shù)下的面積有可能收斂到有限數(shù)。

19：48 這個(gè)標(biāo)誌是希臘字母伽瑪。它通常在數(shù)學(xué)中用于表示階乘函數(shù)的分析延續(xù)。所以基本上它是階乘的，但對(duì)于所有實(shí)數(shù)。

20：28 我不太確定那個(gè)公式是什么，但我認(rèn)為這是拓?fù)鋵W(xué)中的某個(gè)公式，e^ipi 正在增加維度或其他東西，并將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.