H S M Coxeter (1907-2003), aka "Donald", was a geometer: a mathematician who explores space and shape, distance and direction. King of Infinite Space, Siobhan Roberts' biography (2006), is a delightful ramble through the space and shape of Coxeter's life. Rather like that life, Roberts' book is long, well-written, precise, diverse, and quite quirky at times. And like that life, Roberts' book defies encapsulation. Perhaps best would be just to show something that's not even in it: a picture of a pattern that Coxeter generalized, his "loxodromic sequence":

The circle marked "0" touches the three larger ones (numbers 1, 2, 3) and the three smaller ones (-1, -2, -3). And the sequence extends to infinity in both directions: ever-larger and ever-smaller circles, radii in a Golden Ratio. Each kisses the three before and the three after it, in a dizzying spiral. Wow!

_{(cf Hobbes and Geometry (2008-03-04), Genius at Play (2018-11-04), Certain Uncertainty (2021-03-16), Geometric Folding Algorithms (2024-05-18), ...) - ^z - 2025-01-24}