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October 2009

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31 discussions

Geometries, irrationals (was Re: thought re graphing calculators ...)
by Edward Cherlin Oct. 1, 2009

Oct. 1, 2009

>>> Could we develop a geometry which does not depend on the metaphysics >>> of real numbers, continuity, infinity? Or still have infinity, but >>> make it more like Poincare's, a direction (like a time axis). >> >> There are vast realms of such geometries, going back to projective >> geometries over finite fields and the like, and to general topology. >> Lie groups (including the one-point compactification of the complex >> plane) and Lie algebras. Banach spaces. Measure theory. Spaces of >> fractal dimension. Minkowski space. Differential geometry of >> Einsteinian spacetime. Non-commutative geometries in quantum mechanics >> (von Neumann algebras over Hilbert space). Many more. > > A feature we're looking for is "accessible to grade schoolers" i.e. we > don't want you already out the other end of some lengthy pipeline > wherein brainwashing has already occurred. Spherical geometry. The trig gets a bit complicated, but even in kindergarten children can see that an octant of a sphere is a triangle with three right angles. As long as you don't bring in the big words. > I understand that some > elite schools get into jiggering with the fifth postulate (Euclid's) > even pre-college, That's doing it the hard way. > <debate> > > Resolved: "Irrational numbers are of course morally superior to the > rationals as all the best constants (e, phi, pi) are irrational, even > transcendental if we're lucky." I'll see your e, phi, and pi, and raise you 0, 1, -1, and i. e^i*pi + 1 = 0 Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk. The integers were made by God. All else is the work of man.--Kronecker > Pro, con or stand aside? Come prepared next Tuesday. > > </debate> >>> Kirby > > Or you could say Phi (golden mean) is the Phirst Phractal (certainly > the recursivity is there in the algebra). > > Kirby Urner > ндсжег воss > >> >> -- >> Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin >> Silent Thunder is my name, and Children are my nation. >> The Cosmos is my dwelling place, the Truth my destination. >> http://earthtreasury.org/ >> > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://earthtreasury.org/

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