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Quadratrix

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A plane curve used for the solution of the problem of the quadrature of the circle. For example: the dinostratus quadratrix, the cochleoid, the Tschirnhaus quadratrix:

$$y=a\sin\frac{\pi x}{2a},$$

and the Ozanam quadratrix:

$$x=2a\sin^2\frac{y}{2a}.$$


Comments

The dinostratus quadratrix is also called the Hippias quadratrix.

References

[a1] Th.L. Heath, "A history of Greek mathematics" , 1–2 , Dover, reprint (1981)
[a2] M. Kline, "Mathematical thought from ancient to modern times" , Oxford Univ. Press (1972)
[a3] B.L. van der Waerden, "Science awakening" , 1 , Noordhoff (1975) (Translated from Dutch)
[a4] F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
How to Cite This Entry:
Quadratrix. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Quadratrix&oldid=33952
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article