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

这些滑块配置都是 4D 空间中：四数字。

Every intersection point corresponds  with some quadruplet of points.

交都对应于些四组。

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辅助生殖技术，使卵巢排出更多卵子，就可能怀上三胎或四胎。

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些特殊四元组映射到三维空间，不断地将数字与些三元组相关联，那么定会发生些对映碰撞。

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.

也许如果幸运，可能会注意到以下件事：交都与外部四组唯关联。

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.

对于给定四联体，查看它们之间两种对角线，它们将在圆内相交，并且反之亦然。

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.

回答这问题函数称为“n select 4”，根据定义，它计算大小为 N 集合中四联体数量，计算方法与我们之前看到类似。

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能力对于数学来说非常有用，但这只是笑话 - 因为当你开始提出有关四元组、五元组或 100 数字元组问题时，这会令人沮丧。