1. So, what's the idea of spherical coordinates?

2. And, you switch it into spherical coordinates.

3. The Laplacian in the columnar and spherical coordinates is deduced by using the derivative principle of the multivariable functions.

4. So now we're going to triple integrals in spherical coordinates.

5. Well, spherical coordinates become appealing because the function you are averaging is just rho while in other coordinate systems it's a more complicated function.

6. Spherical coordinates are a way of describing points in space in terms of three variables.

7. The variable or distance to the origin in spherical coordinates.

8. So, one is, these are called spherical coordinates because if you fix the value of rho, then you are moving on a sphere centered at the origin.

9. But let's do it in spherical coordinates because that's the topic of today.

10. And, now we have to learn about spherical coordinates, which you will see are a lot of fun.

11. That will give you a good idea of what kinds of things we've seen in spherical coordinates.

12. And, the surface element on a sphere, so, see, it's very closely related to the volume element of spherical coordinates except you don't have a rho anymore.

13. So, if you are asked to find the average distance from the origin, spherical coordinates can be interesting.

14. So,[Sentence dictionary] it's much better to set up these integrals in spherical coordinates.

15. And, of course, you will actually do that in spherical coordinates because it is easier that way.

16. Well, we have to figure out how to set up our triple integral in spherical coordinates.

17. We have rectangular coordinates, we have cylindrical coordinates and we have spherical coordinates.

18. OK, so note how the equation of this horizontal plane in spherical coordinates has become a little bit weird.

19. There we want to think a tiny bit about spherical coordinates again.

20. Now, it is OK to think of them as spherical coordinates, but I would like to encourage you not to think of them as spherical coordinates.

21. The helical surface equations of the spherical hob are set up in spherical coordinates. The formulas of the side clearance angle and numerical examples are given.