Category: Geometry Page 17 of 168

Abuse of Language

From Wikipedia — Abuse of language — “… in mathematics, a use of terminology in a way that is not formally correct but that simplifies exposition or suggests the correct intuition.” The phrase “symplectic…

Symplectic Structure*

From Gotay and Isenberg, "The Symplectization of Science," Gazette des Mathématiciens  54, 59-79 (1992): "… what is the origin of the unusual name 'symplectic'? …. Its mathematical usage…

A Wrinkle in Space

"There is  such a thing as a tesseract." — Madeleine L'Engle An approach via the Omega Matrix: See, too, Rosenhain and Göpel as The Shadow Guests .

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…

The Diamond-Theorem Correlation

Click image for a larger, clearer version.

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…

George Johnson's Theory of Everything

George Johnson, a science writer, in The New York Times on July 21, 2014: “New particles may yet be discovered, and even new laws. But it is almost…

Sunday School

Paradigms of Geometry: Continuous and Discrete The discovery of the incommensurability of a square's side with its diagonal contrasted a well-known discrete  length (the side) with a new continuous  length (the diagonal). The figures below…

Paradigm Shift:

  Continuous Euclidean space to discrete Galois space* Euclidean space: From a page by Bryan Clair Counting symmetries in Euclidean space: Galois space: Counting symmetries of  Galois space: The…

Finite Jest

(Continued from a private post of May 27, 2012)