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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 ...
The most basic example is the p-adic valuation ν p associated to a prime integer p, on the rational numbers =, with valuation ring = (), where is the localization of at the prime ideal (). The valuation group is the additive integers Γ = Z . {\displaystyle \Gamma =\mathbb {Z} .}
In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables.
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 ...
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
Real numbers were called "proportions", being the ratios of two lengths, or equivalently being measures of a length in terms of another length, called unit length. Two lengths are "commensurable", if there is a unit in which they are both measured by integers, that is, in modern terminology, if their ratio is a rational number.
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.