Difference between revisions of "Quadratrix"
From Encyclopedia of Mathematics
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A plane curve used for the solution of the problem of the [[Quadrature of the circle|quadrature of the circle]]. For example: the [[Dinostratus quadratrix|dinostratus quadratrix]], the [[Cochleoid|cochleoid]], the Tschirnhaus quadratrix: | A plane curve used for the solution of the problem of the [[Quadrature of the circle|quadrature of the circle]]. For example: the [[Dinostratus quadratrix|dinostratus quadratrix]], the [[Cochleoid|cochleoid]], the Tschirnhaus quadratrix: | ||
| − | + | $$y=a\sin\frac{\pi x}{2a},$$ | |
and the Ozanam quadratrix: | and the Ozanam quadratrix: | ||
| − | + | $$x=2a\sin^2\frac{y}{2a}.$$ | |
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> Th.L. Heath, "A history of Greek mathematics" , '''1–2''' , Dover, reprint (1981)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Kline, "Mathematical thought from ancient to modern times" , Oxford Univ. Press (1972)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> B.L. van der Waerden, "Science awakening" , '''1''' , Noordhoff (1975) (Translated from Dutch)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top"> F. Gomes Teixeira, "Traité des courbes" , '''1–3''' , Chelsea, reprint (1971)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> Th.L. Heath, "A history of Greek mathematics" , '''1–2''' , Dover, reprint (1981)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Kline, "Mathematical thought from ancient to modern times" , Oxford Univ. Press (1972)</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> B.L. van der Waerden, "Science awakening" , '''1''' , Noordhoff (1975) (Translated from Dutch)</TD></TR> | ||
| + | <TR><TD valign="top">[a4]</TD> <TD valign="top"> F. Gomes Teixeira, "Traité des courbes" , '''1–3''' , Chelsea, reprint (1971)</TD></TR> | ||
| + | </table> | ||
| + | |||
| + | [[Category:Geometry]] | ||
Latest revision as of 18:18, 19 October 2014
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://encyclopediaofmath.org/index.php?title=Quadratrix&oldid=11478
Quadratrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadratrix&oldid=11478
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article