Over time, people worked out a general formula for the numbers in Pascal's triangle.

随着时间的流逝，人们为帕斯卡三角形中的数字制定了一个通用公式。

It's gonna be around well after we're gone and ancient civilizations, alien civilizations we'll know Pascal's triangle.

在我们和古代文明消失之后，它还会继续存在，外星文明我们就会知道帕斯卡三角形。

Exactly, there's even a continuum of Pascal's triangles, between zero and one there's this a continuum of numbers that you could put in for powers.

- 没错，甚至还有帕斯卡三角形的连续体，在零和一之间有一系列数字，你可以用它们来表示幂。

That makes me think that we could actually go into Pascal's triangle blow it up and add fractions in between the rows that we're familiar with.

- 这让我认为我们实际上可以进入帕斯卡三角形，把它炸毁，并在我们熟悉的行之间添加分数。

If you look at the numbers in these equations the coefficients on X and X squared and so on, well, they're actually just the numbers in Pascal's triangle.

如果你看一下这些方程中的数字，X 的系数和 X 的平方等等，嗯，它们实际上只是帕斯卡三角形中的数字。

So Newton is convinced the binomial theorem works even for negative values of N, which means there's more to Pascal's triangle above the zeroeth you could add a zero and a one that add to make that first one.

因此，牛顿确信二项式定理即使适用于 N 的负值，这意味着帕斯卡三角形中除了零之外还有更多内容，您可以添加一个零和一个一，将它们相加得到第一个。