Cartesian geometry is not merely inconvenient, but wrong enough so that it's actively hindering our civilization. It's a blind alley, in the same way Roman numerals were.
Buckminster Fuller's most startling inventions are trivial exercises of the theory in this book.
Sorry to sound hysterical, but this is a really important book, and it's much too neglected. It should definitely NOT be out of print. It's right up there with Euclid. Fuller was a genius, but he couldn't write. Edmondson can.
Amy Edmondson worked closely with Buckminster Fuller before he died. She extracted, and explains in this book Fuller's least tractable, least appreciated concepts: His realization that the natural analytic geometry of the universe is tetrahedral. This is the stuff that people were forming study groups to try to extract from "Synergetics," and she just lays it out, in neat, logical prose with clear diagrams, and references to related scholarly literature...
Fuller (according to Edmondson) ran into tetrahedral geometry by no less than three different routes: close packing of spheres, three dimensional stabilization of an object by either compressive or tensile members. Then, as a trivial exercise, a result, there's a proof that the maximum strength homogenous truss is tetrahedral. Then, almost as an aside, it happens that all the regular solids (except the icosahedron) have volumes that are integral multiples of the volume of a tetrahedron!
Right about then, I began to think that everything I know about geometry is, not wrong eactly, but just not the right way. You know, like finding arabic numerals when you've been using roman numerals your whole life.
I was totally blown away, and I was expecting to be bored spitless.
If you're interested in Buckminster Fuller's work, GET THIS BOOK!
If you're a mathematician, GET THIS BOOK!!!