Books, Books, and More Books

It's lazy, I know, just to give a list of books, but here it goes anyway: I've been trying to understand foundational issues in geometry, and John Stillwell's book "The Four Pillars of Geometry" is terrific. It's strange that I could get through grad in math, and not understand how to take a square root geometrically.

Also Farin's book on "NURBS" is typeset wonderfully (probably using TeX) and is a pleasure to read.

NURBS

I have found a focus for my mathematical work for a while: I am going to read a book on NURBS. I know it's not foundational, but I hope to learn enough to motivate me to later study of algebraic geometry, or CAD, or both.

Very basic mathematics

I am still trying to understand trig functions and the exponential and log functions. That is, really understand their essence in a Zen sort of way.

Going back to Euler, you really have to use infinite series, and even infinitesimals, I think.

Time and Space!

A conversation on another blog has me thinking about the difference between multiplication and addition.

Somewhere I've seen a discussion, maybe in Lawvere?, of multiplication being more "natural" than addition. The categorical product is available in more categories than the categorical coproduct, I think.

Alexandre Borovnik suggests that since time intervals are not multiplied, but are added and compared, tropical mathematics is more natural for time and concurrency than ordinary arithmetic. Tropical mathematics replaces ordinary "x and +" with "+ and max", where max gives the larger of two numbers.