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

球心到球面上任何一点的距离都一样。

That's also of great value scientifically.

这个外球面区域的科学研究意义很大。

The research was based on pulsar timing observations carried out with the Five-hundred-meter Aperture Spherical Telescope (FAST).

这项研究是基于500米口径球面望远镜(FAST)进行的脉冲星计时观测。

To prove the theorem we shall suppose that the graph G is drawn on a sphere as described above.

为了证明这个定理，我们假定这个圆G能按上画在一个球面上。

Spherical reflectors don't perfectly focus all the incoming rays.

球面不能完美地聚焦所有入光线。

It's a pseudosphere, for the curvature of the Earth.

这是一个伪球面，用于模拟地球的曲率。

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

dA的积分是A；即同心球面的面积。

Well, first let's like linger on the spheres and the light cones.

好吧，首先让我们先关注一下球面和光锥。

And the way to think about that is just the surface of a sphere.

可以这样想，那就是一个球面。

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。

So, the electric flux is independent of the  radius of the concentric spherical surface?

所以，电通量与同心球面的半径无关？

Now, we wanna talk about the product of two spheres.

现在，我们想谈谈两个球面的乘积。

The discovery was made using the Five Hundred  Meter Aperture Spherical Radio Telescope, or the FAST telescope.

这一发现是由五百米口径球面电望远镜，即FAST望远镜实现的。

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， 你可以看到这一点。

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。

Points on the exact opposite side of a sphere are called " antipodes" , or " antipodal points" .

球面上完全相对的点称为“对跖点”或“对跖点”。

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法来除以 0，但今天我们且不谈这个。

It's not too hard to see that all those possible  normal vectors trace out the surface of a sphere.

不难看出，所有这些可能的法向量会描绘出一个球面。

Rather than using a parabolic shape for the dish that would focus everything to a single point, they chose a spherical curve.

与其使用将所有东西聚焦到一个点的抛物面形状，他们选择了一个球面曲线。

So, as a spherical wave moves farther from its source, its intensity will decrease by the square of the distance from it.

因此，随着球面波远离其源，其强度将按距其距离的平而减小。