Category: Geometry Page 5 of 168

Logic

Seven years ago in this journal — The above links:  the Stone,  the rules.

Harrowing of Hell (continued)

Holy Saturday is, according to tradition, the day of  the harrowing of Hell. Notes: The above passage on "Die Figuren der vier Modi im Magischen Quadrat " should be…

Würfel-Märchen

Continued from yesterday, the date of death for German billionaire philanthropist Klaus Tschira — For Tschira in this journal, see Stiftung . For some Würfel  illustrations, see this morning's post Manifest O.  A…

Math's Big Lies

Two mathematicians, Barry Mazur and Edward Frenkel, have, for rhetorical effect, badly misrepresented the history of some basic fields of mathematics. Mazur and Frenkel like to emphasize the…

Manifest O

The title was suggested by http://benmarcus.com/smallwork/manifesto/. The "O" of the title stands for the octahedral  group. See the following, from http://finitegeometry.org/sc/map.html — 83-06-21 An invariance of symmetry The diamond theorem on a…

The Möbius Hypercube

The incidences of points and planes in the Möbius 84  configuration (8 points and 8 planes, with 4 points on each plane and 4 planes on each point), were described by Coxeter in…

Hirzebruch

(Continued from July 16, 2014.) Some background from Wikipedia: "Friedrich Ernst Peter Hirzebruch  ForMemRS[2]  (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology,  complex…

Brouwer on the Galois Tesseract

Yesterday's post suggests a review of the following — Andries Brouwer, preprint, 1982: "The Witt designs, Golay codes and Mathieu groups" (unpublished as of 2013) Pages 8-9: Substructures…

Gallucci's Möbius Configuration

From H. S. M. Coxeter's 1950 paper "Self-Dual Configurations and Regular Graphs,"  a 4×4 array and a more perspicuous rearrangement— (Click image to enlarge.)  The above rearrangement brings Coxeter's…

Focus!

A sequel to Dude! See also "Triangles are Square."