Area of a sphere explained beautifully!

The beautiful integration. Let us go through each picture of the GIF step by step.

1. You originally see a sphere.
2. The sphere meshes in many pieces.
3. It then explodes and simultaneously changes from 3 dimensions to 2 dimensions.
4. The upper half becomes the positive part of the sine wave.
5. The lower half becomes the negative part of the sine wave.
6. This sine wave is then integrated over the axis it is projected on.(in this case the x-axis)
7. And magic: You get the area of the sphere which IS 4*pi*r squared.