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Like the sine, the cosine and tangent are replaced with rational equivalents, called the "cross" and "twist", and Divine Proportions develops various analogues of trigonometric identities involving these quantities, [3] including versions of the Pythagorean theorem, law of sines and law of cosines. [4]
Having attending several of Norman Wildeberger's talks, the rationale behind rational trigonometry is that the concept of an angle belongs to a circle (ie, Euler's formula), and that the concept of spread is far more natural for a triangle (c.f. Thales' theorem). Angles and distance also break down in fields other than the real numbers, whereas ...
I just created this article, because Wildberger clearly needed an article, as he has made an important contribution to mathematics with his new subject known as "rational trigonometry."Dratman 01:56, 17 September 2011 (UTC) I think there have been changes since the Wikipedia:Articles for deletion/Norman J. Wildberger discussion. Wildberger is ...
Dirichlet's theorem on arithmetic progressions. In 1808 Legendre published an attempt at a proof of Dirichlet's theorem, but as Dupré pointed out in 1859 one of the lemmas used by Legendre is false. Dirichlet gave a complete proof in 1837. The proofs of the Kronecker–Weber theorem by Kronecker (1853) and Weber (1886) both had gaps. The first ...
Wildberger is a surname. Notable people with the surname include: Ed Wildberger, Missouri politician; Jacques Wildberger, Swiss composer; Norman J. Wildberger, mathematician known for rational trigonometry; Tina Wildberger, Hawaii politician
The theorem extends to the other trigonometric functions as well. [2] For rational values of θ, the only rational values of the sine or cosine are 0, ±1/2, and ±1; the only rational values of the secant or cosecant are ±1 and ±2; and the only rational values of the tangent or cotangent are 0 and ±1. [3]
Lüroth's problem concerns subextensions L of K(X), the rational functions in the single indeterminate X. Any such field is either equal to K or is also rational, i.e. L = K(F) for some rational function F. In geometrical terms this states that a non-constant rational map from the projective line to a curve C can only occur when C also has genus 0.
A well-known example is the Taniyama–Shimura conjecture, now the modularity theorem, which proposed that each elliptic curve over the rational numbers can be translated into a modular form (in such a way as to preserve the associated L-function). There are difficulties in identifying this with an isomorphism, in any strict sense of the word.