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In mathematics, a transcendental curve is a curve that is not an algebraic curve.〔Newman, JA, ''The Universal Encyclopedia of Mathematics'', Pan Reference Books, 1976, ISBN 0-330-24396-9, "Transcendental curves".〕 Here for a curve, ''C'', what matters is the point set (typically in the plane) underlying ''C'', not a given parametrisation. For example, the unit circle is an algebraic curve (pedantically, the real points of such a curve); the usual parametrisation by trigonometric functions may involve those transcendental functions, but certainly the unit circle is defined by a polynomial equation. (The same remark applies to elliptic curves and elliptic functions; and in fact to curves of genus > 1 and automorphic functions.) The properties of algebraic curves, such as Bézout's theorem, give rise to criteria for showing curves actually are transcendental. For example an algebraic curve ''C'' either meets a given line ''L'' in a finite number of points, or possibly contains all of ''L''. Thus a curve intersecting any line in an infinite number of points, while not containing it, must be transcendental. This applies not just to sinusoidal curves, therefore; but to large classes of curves showing oscillations. The term is originally attributed to Leibniz. == Further examples == * Cycloid * Trigonometric functions * Logarithmic and exponential functions * Archimedes' spiral * Logarithmic spiral * Catenary * Tricomplex cosexponential 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「transcendental curve」の詳細全文を読む スポンサード リンク
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