In mathematics, specifically in the area of hyperbolic geometry, Hilbert's arithmetic of ends is a method for endowing a geometric set, the set of ideal points or "ends" of a hyperbolic plane, with an algebraic structure as a field. It was introduced by German mathematician David Hilbert.
Read more about Hilbert's Arithmetic Of Ends: Rigid Motions
Famous quotes containing the words arithmetic and/or ends:
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“Great Negative, how vainly would the Wise
Enquire, define, distinguish, teach, devise,
Didst thou not stand to point their dull Philosophies?
Is, or is not, the two great Ends of Fate,
And, true or false, the Subject of Debate,
That perfect, or destroy, the vast Designs of Fate,”
—John Wilmot, 2d Earl Of Rochester (1909–1969)