There is an exciting relatively new area in mathematics called tropical geometry. If I understand it correctly, the idea here is to redefine the “sum” of two real numbers as their minimum, and the “product” as their usual sum (it is possible to use the maximum instead of the minimum as well). So:
- x ⊕ y = min(x, y)
- x ⊗ y = x + y
I agree this looks rather crazy, but that’s what makes the subject fascinating! For example, [these] beautiful drawings are graphs of polynomials of degree three, tropical cubic curves (in fact, they are elliptic curves).
Here is what a second-degree curve looks like:
As Pi Day approaches, it time for a refresher course, courtesy of Steven Strogatz, on what pi actually means and how you can visualize calculating it. It’s all about rearranging the pieces of a circle in a calculus-ish sort of way: