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Rational trigonometry: computational viewpoint. (English) Zbl 1161.26008

In the book of [N. J. Wildberger, Divine Proportions: Rational Trigonometry to Universal Geometry. (Kingsford): Wild Egg. (2005; Zbl 1192.00004)] it is shown that if we characterize each side \(a_{i}\) of a triangle by its “quadrance” \( s_{i}:=a_{i}^{2}\) and each angle \(A_{i}\)by its “spread” \(Q_{i}:=\sin ^{2}(A_{i}),\) then all the formulas for solving triangles become algebraic. Formulas using \(s_{i}\) and \(Q_{i}\) are called rational trigonometry. The author shows that rational trigonometry is the computationally fastest way of solving triangles.

MSC:

26D05 Inequalities for trigonometric functions and polynomials
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions

Citations:

Zbl 1192.00004
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