Tag: Geometry Page 1 of 7

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…

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…

Symplectic Structure continued

Some background for the part of the 2002 paper by Dolgachev and Keum quoted here on January 17, 2014 — Related material in this journal (click image for posts) —

The Omega Matrix

Shown below is the matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1976-1979) by Steven H. Cullinane. Backstory:  The Schwartz Notes (June 1, 2011), and…

Zero System

The title phrase (not to be confused with the film 'The Zero Theorem') means, according to the Encyclopedia of Mathematics, a null system , and "A null system is…

Three Constructions of the Miracle Octad Generator

See also a Log24 post on this subject from Dec. 14, 2013, especially (scroll down) the update of March 9, 2014. Related material on the Turyn-Curtis construction from the…

Classical Galois

Click image for more details. To enlarge image, click here.

The Representation of Minus One

For the late mathematics educator Zoltan Dienes. "There comes a time when the learner has identified the abstract content of a number of different games and is practically…

The 4×4 Relativity Problem

The sixteen-dot square array in yesterday’s noon post suggests the following remarks. “This is the relativity problem:  to fix objectively a class of equivalent coordinatizations and to ascertain…

For Emil Artin

(On His Dies Natalis )… An Exceptional Isomorphism Between Geometric and Combinatorial Steiner Triple Systems Underlies  the Octads of the M24 Steiner System S(5, 8, 24). This is asserted in an excerpt from…  "The…