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Discrete differential geometry Check out page 40 of the source PDF (calcula ex geometrica) — they talk about geometrical computation. Instead of approximating analog with digital doing digital arithmetic smoothing the result to fake an analog again why not OOP-define … Continue reading
Tagged curves, differential forms, differential geomtery, discrete differential geometry, Elie Cartan, exterior calculus, exterior derivative, geometry, math, mathematics, maths, object-oriented programming, piecewise linear
In philosophical debates about absolute truth, people cite “the truths of pure mathematics” as beyond reproach—eternal and universal things discovered/invented by us fallible mortals. But the more deeply I look into these issues myself, the more I see evidence that … Continue reading
June 23, 2012
Tagged angle, constructivism, dispute, field theory, Galois field extensions, Galois theory, geometry, intelligence, judgmental, logic, math, mathematics, maths, Norman J. Wildberger, philosophy, spread, truth, unpopular
I normally discard all homework questions (I get a lot). But georgiatehc is a cool kid and has been a loyal tumblr follower for quite a long time. So I wrote him a long answer summarising the spiel I used … Continue reading
Posted in Uncategorized
Tagged combinatorics, education, homework, math help, math teacher, math tutor, mathematics, maths help, order doesn't matter, order matters, school, teaching, word problems
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derivatives of Gaussian PDF’s
Why bicontinuity is the right condition for topological equivalence (homeomorphism): if continuity of the inverse isn’t required, then a circle could be equivalent to a line (.99999 and 0 would be neighbours) — Minute 8 or so. Geometric construction (no … Continue reading
June 12, 2012
Tagged algebra, bicontinuity, continuity, Desargues' theorem, geometry, group theory, homeomorphism, mathematics, Pappos' theorem, Pascal's theorem, projective geometry, projective plane, topological algebra, topology
One way to think about quantum operators is as Questions that are asked of a quantum system. Identity operator = “Who are you?” Energy operator = “How much do you weigh?” “What is your spin along the z axis?” and … Continue reading