The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Archive). It can be used for angle
trisection or, more generally, division of an angle
into any integral number of equal parts, and circle
squaring .

It has polar equation

(1)

with corresponding parametric equation

and Cartesian equation

(4)

Using the parametric representation, the curvature
and tangential angle are given by

for .

See also Angle trisection ,

Cochleoid
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References Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 223,
1987. Lawrence, J. D. A
Catalog of Special Plane Curves. New York: Dover, pp. 195 and 198, 1972. Loomis,
E. S. "The Quadratrix." §2.1 in The
Pythagorean Proposition: Its Demonstrations Analyzed and Classified and Bibliography
of Sources for Data of the Four Kinds of "Proofs," 2nd ed. Reston,
VA: National Council of Teachers of Mathematics, pp. 19-20, 1968. Loy,
J. "Trisection of an Angle." http://www.jimloy.com/geometry/trisect.htm#curves . MacTutor
History of Mathematics Archive. "Quadratrix of Hippias." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Quadratrix.html .
Cite this as:
Weisstein, Eric W. "Quadratrix of Hippias."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/QuadratrixofHippias.html

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