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In integral calculus, the Weierstrass substitution or tangent half-angle substitution is a method for evaluating integrals, which converts a rational function of trigonometric functions of x into an ordinary rational function of t by setting t = \tan (x /2).Weisstein, Eric W.
In geometry, a tile substitution is a method for constructing highly ordered tilings. Most importantly, some tile substitutions generate aperiodic tilings, which are tilings whose prototiles do not admit any tiling with translational symmetry.
In integral calculus, the tangent half-angle substitution – known in Russia as the universal trigonometric substitution, p. 379 sometimes misattributed as the Weierstrass substitution,James Stewart mentioned Karl Weierstrass when discussing the substitution in his popular 1987 calculus textbook: