Category: Geometry Page 17 of 168
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…
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…
"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 .
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…
Click image for a larger, clearer version.
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, 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…
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…
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…
(Continued from a private post of May 27, 2012)