On 9 December 2024 I gave a talk in the NUS Topology, Geometry and Dynamics seminar. It was entitled “Spinors and lambda lengths”.
Spinors and Descartes’ Theorem
Descartes’ circle theorem relates the curvatures of four mutually externally tangent circles, three “petal” circles around the exterior of a central circle, forming a “3-flower” configuration. We generalise this theorem to the case of an “n-flower”, consisting of n tangent circles around the exterior of a central circle, and give an explicit equation satisfied by their curvatures. The proof uses a spinorial description of horospheres in hyperbolic geometry.
Spinors and Horospheres, Monash topology seminar, April 2023
On 26 April 2023 I gave a talk in the Monash topology seminar. It was entitled “Spinors and horospheres”.
One line Euler line
A fun fact from Euclidean geometry that I thought was a wonderful enough gem to share. It’s standard, but it’s nowhere near any curriculum. I’ll try not to get too snarky about the curriculum.