Differential Geometry

From my office window I can study the lonely geometry of the Falcon's gyre, but were I to turn my attention away from the distractions of Japanese nature for a moment to my work (mathematics) I can find many strange and entertaining objects to distract me within my little study. It would appear that the original owner of this room (before it became the foreign research students' room) was a mathematician who studied Differential Geometry, and here I present to you two of the methods he used to teach his topic. In my next post you will see strong evidence that he was teaching before the advent of the computer, so he had to use models. There is a bookcase full of these models in my room, all packed neatly in wooden boxes with their equations on the lid. There are also two models made of wood and string sitting free on the bookcase, one looking for all the world like a multi-dimensional Aussie cork hat and the other presented here.

The wood and string model here could be a saddle point from dynamics, but I think it is meant to represent one of the conical sections and I'm buggered if I can remember which one. In front of it we have a 3-dimensional ellipse, which was actually still wobbling when I took the photo. We have other conical sections and slices in the boxes, as well as some weird bottles with beads in which are I think for selecting random numbers, the afore-mentioned multi-dimensional aussie cork hat, and some random numbered discs. It reminds me of a mathematical version of those classes you had when you were at high school, sticking together molecules from different coloured polystyrene balls. Thank the Gods of Reason for the invention of computer graphics!!!