Multiplying by i…
Recently I did a series of posts about how the complex numbers arise from a natural progression of math realizations. I’ve done posts in the past about how the natural numbers lead through the integers and rationals to the real numbers. (And I’ve done posts about how weird the real numbers are, but that’s another topic.)
I recently came across another way a progression of obvious natural questions directly leads to the necessity of a new type of number, and this progression takes us all the way from the naturals to the complex numbers.
All by asking, “What do you get when you…”
In my family, we were rather casual about birthdays and other event days. It wasn’t unusual to celebrate a birthday, not on the exact day, but on a nearby day. We were fairly poor, so birthdays mostly consisted of a cake and a token present of some sort. (Put it this way: I can’t recall a single birthday present I ever got. We just weren’t that into birthdays.)
Logos con carne 