Each configuration of these sliders is a point in 4D space: A quadruplet of numbers.

这滑块的每个配置都是 4D 空间中的个点：个数字。

Every intersection point corresponds  with some quadruplet of points.

每个交点都对应于组点。

But if you use different types of assisted reproductive technology that make your ovaries excrete more eggs, you might get pregnant with triplets or quadruplets.

但如果使用其他类型的辅助生殖技术，使卵巢排出更多的卵子，就可能怀上三胎或胎。

Maybe if you're a little bit lucky,   here's one thing you might notice; every intersection point is uniquely associated  with a quadruplet of points on the exterior.

也许如果您幸运点，您可能会注意到以下件事：每个交点都与外部的组点唯。

For a given quadruplet, you look at the  two kind of diagonal cords between them and those will intersect within the circle  and it goes the other way around.

对于给定的体，您查看它们之间的两种对角线，它们将在圆内相交，并且反之亦然。

Borsuk-Ulam says that if you try to map that set, all those special quadruplets, into 3-dimensional space, continuously associating each one some triplet of numbers, there must be some antipodal collision.

Borsuk-Ulam 说，如果你尝试将所有这特殊的元组映射到三维空间，不断地将每个数字与三元组相，那么定会发生对映碰撞。

There is no doubt that the ability to frame analytic facts geometrically is very useful for math But it's all a tease - because when you start asking questions about quadruplets or quintuplets or 100 tuples of numbers It's frustrating.

毫无疑问，以几何方式构建分析事实的能力对于数学来说非常有用，但这只是个笑话 - 因为当你开始提出有元组、五元组或 100 个数字元组的问题时，这会令人沮丧。

The function that answers it is called " n choose 4" which by definition  counts the number of quadruplets from a set of size N and the way to calculate it is similar  to what we saw before.

回答这个问题的函数称为“n select 4”，根据定义，它计算大小为 N 的集合中体的数量，计算方法与我们之前看到的类似。