let's focus on good definitions...” Today, I'll explore a seemingly simple question: what is a rotation? I'm asking for the definition of a rotation, which »

On the last post, I gave a naive idea of where the Jacobian determinant comes from when changing variables: it was the volume of an approximate »

Years ago I used the Jacobian determinant to find the area of an astroid and made a note about finding out where it came from. There »

In the beginning, there was nothing, $$0 = \emptyset$$. Then we realized it was something, $$1 = \{ \emptyset \}$$. Then we wondered, why not have another thing? $$2$$. And »