12/3/13 Quadratrix of Hippias -- from Wolfram MathWorld Search MathWorld Algebra Applied Mathematics Geometry > Curves > Plane Curves > Polar Curves > Geometry > Geometric Construction > Calculus and Analysis Interactive Entries > Interactive Demonstrations > Discrete Mathematics THINGS TO TRY: Quadratrix of Hippias quadratrix of hippias Foundations of Mathematics 12-w heel graph Geometry d^4/dt^4(Ai(t)) History and Terminology Number Theory Probability and Statistics Recreational Mathematics Hippias Quadratrix Bruno Autin Topology Alphabetical Index Interactive Entries Random Entry New in MathWorld MathWorld Classroom About MathWorld The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Contribute to MathWorld Archive). It can be used for angle trisection or, more generally, division of an angle into any integral number of equal Send a Message to the Team parts, and circle squaring. It has polar equation MathWorld Book (1) Wolfram Web Resources » 13,191 entries with corresponding parametric equation Last updated: Wed Nov 6 2013 (2) Created, developed, and nurtured by Eric Weisstein at Wolfram Research (3) and Cartesian equation (4) Using the parametric representation, the curvature and tangential angle are given by (5) (6) for . SEE ALSO: Angle trisection, Cochleoid REFERENCES: Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 223, 1987. Law rence, 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://w w w .jimloy.com/geometry/trisect.htm#curves. MacTutor History of Mathematics Archive. "Quadratrix of Hippias." http://w w w -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. http://mathw orld.w olfram.com/QuadratrixofHippias.html Wolfram Web Resources Mathematica » Wolfram|Alpha » Wolfram Demonstrations Project » The #1 tool for creating Explore anything with the first Explore thousands of free applications Demonstrations and anything computational knowledge engine. across science, mathematics, technical. engineering, technology, business, art, finance, social sciences, and more. mathworld.wolfram.com/QuadratrixofHippias.html 1/2 12/3/13 Quadratrix of Hippias -- from Wolfram MathWorld finance, social sciences, and more. Computable Document Format » STEM initiative » Computerbasedmath.org » The format that makes Programs & resources for Join the initiative for modernizing math Demonstrations (and any educators, schools & students. education. information) easy to share and interact with. Contact the MathWorld Team © 1999-2013 Wolfram Research, Inc. | Terms of Use mathworld.wolfram.com/QuadratrixofHippias.html 2/2.