That's also of great value scientifically.

这个外球面区域的科学研究意义很大。

The integral of dA is A; the area of the concentric spherical surface.

dA的A;同心球面的面。

All points on the surface of a sphere are equally distant from the center.

球心到球面上任何一的距离都一样。

Say we have a lens that has a spherical face on both sides, known as a convex lens.

假设我们有一个具有球面的镜头 两侧，称为凸透镜。

And then you have another spherical wave coming from the short bank.

然后你会看到另一个来自短波岸的球面波。

And you can see this when the ball back by the spread-out lines of oil on the ball surface.

当球从球面上的油线中滚回时， 你可以看到这一。

As an example, Borsuk-Ulam also applies to mapping hyperspheres in 4d space into 3d space.

例如，Borsuk-Ulam 还适用于将 4d 空间中的超球面映射到 3d 空间。

There actually is something called the Riemann sphere that involves dividing by zero by a different method, but that's a story for another day.

事实上，有个叫黎曼球面的东西，它涉及到通过不同的方法来除以 0，但今天我们且不谈这个。

Initially the telescope used line feeds, elongated receivers that could gather signals within the focal line of the spherical dish.

最初， 望远镜使用线馈送，细长的接收器可以收集球面盘焦线内的信。

Actually, the electric field has the  same magnitude as it passes through every infinitesimally small area, dA, on the  concentric, spherical surface through which we are finding the flux.

实际上，当电场穿过我们正在寻找通量的同心球面上的每个无穷小区域 dA 时，它具有相同的幅度。

Geometrically, a four-dimensional creature would be able to look at those two perpendicular rotations that I just described and understand that they lock you into one and only one rigid motion for the hypersphere.

从几何角度来看，四维生物能够看到我刚才描述的这两个垂直旋，并理解它们将你锁定在超球面的一个且唯一一个刚性运动中。

To think about the projection, let's make a little right triangle like this, where what was the height of our spherical rectangle is the hypotenuse, and its projection is one of the legs.

为了考虑投影， 让我们制作一个像这样的小直角三角形，其中球面矩形的高度斜边，它的投影其中一条腿。

What I mean by hypersphere is the set of all possible lists of 4-coordinates where the sum of their squares equals 1; those are points in 4d space a distance 1 from the origin.

我所说的超球面所有可能的 4 坐标列表的集合， 其中它们的平方和等于 1；这些 4d 空间中距离原 1 的。

Here we have the travelling binary numbers which give us a sense of the data being sent, however it also doesn't show the spherical propagation of the electromagnetic waves or the changing frequency of the wave.

这里我们有传播的二进制数， 它让我们了解正在发送的数据，但它也没有显示电磁波的球面传播或波的变化频率。

In the example we just did, capital  Q is the charge of the point charge, and it is the charge enclosed inside an  imaginary spherical surface and the imaginary spherical surface is called a Gaussian surface.

在我们刚才做的例子中， 大写 Q 电荷的电荷，它被包裹在一个假想球面内的电荷， 这个假想球面称为高斯曲面。

Hubble Space Telescope Program Manager Douglas Broome delivered the troubling news: “The conclusion we’ve come to is that a significant spherical aberration appears to be present in the optics, in the optical telescope system optics, ” he said.

哈勃太空望远镜项目经理道格拉斯·布鲁姆 (Douglas Broome) 发布了这个令人不安的消息：“我们得出的结论，光学望远镜系统的光学元件中似乎存在明显的球面像差， ” 他说。