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As a wheel travels in a straight line, the locus of any point on its circumference will be a familiar curve known as a cycloid (click the movie button for a movie). ... My interest in this paper is to see how we may use Geometer's Sketchpad (GSP) as a tool for exploring the properties of these figures. I claim that...
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jwilson.coe.uga.edu/emt668/EMT668.Student.Folders/Bromb...
jwilson.coe.uga.edu/emt668/EMT668.Student.Folders/BrombacherAarnout/EMT669/cycloids/cycloids.html
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Amer. Math. Monthly 50, 309-315, 1948. Yates, R. C. "Cycloid." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 65-70, 1952. ...
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mathworld.wolfram.com/Cycloid.html
mathworld.wolfram.com/Cycloid.html
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The Cycloid Family of Curves ... Galileo and Father Mersenne are credited with being the first to name and discuss its special properties (1599). They were followed by Torricelli, Fermat, Descartes, Roberval, Wren, Huygens, Desargues, Johann Bernoulli, Leibniz, Newton, Jakob Bernoulli, L'Hôpital and others.
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curvebank.calstatela.edu/cycloidmaple/cycloid.htm
curvebank.calstatela.edu/cycloidmaple/cycloid.htm
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Building an Apparatus to Demonstrate Some of the Properties of the Famous Cycloid Curve ; ... A short history and description of the cycloid; A Cycloid Curve is generated by a point on a circle's circumference rolling on a plane. See figures below. The cycloid posses interesting physical properties.
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www.scitechantiques.com/cycloidhtml/
www.scitechantiques.com/cycloidhtml/
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Mersenne gave the first proper definition of the cycloid and stated the obvious properties such as the length of the base equals the circumference of the rolling circle. Mersenne attempted to find the area under the curve by integration but failed.
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www-history.mcs.st-and.ac.uk/Curves/Cycloid.html
www-history.mcs.st-and.ac.uk/Curves/Cycloid.html
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The trace of a point on the circumference is called cycloid. The angle t in the figure is the angle through which the radius turns as the circle rolls to a new position. x=a(t-sin t), y=a(1-cos t); ... Then, the angle by the tangent line of cycloid and the y-axis is equal to t/2. Why? 1. The circle touches x-axis at point...
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www.ies.co.jp/math/java/calc/cycle_ang/cycle_ang.html
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It works best to set Vertices relative to the Cusps property found on the cycloid variation's properties page (see Experiment 2). Set Cusps as a multiple ... Change the cycloid properties. To do this, select the variation's Properties page: ... General; Orbital / IFS / Strange Attractor; Orbit Variation; Cycloid; Properties...
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www.fractalsciencekit.com/tutorial/examples/sierpcy.htm
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The curve is formed by the locus of a point, attached to a circle (cycle -> cycloid), that rolls along a straight line 1). ... (ordinary) cycloid; The starting point is situated on the circle (a = 1). When the starting point is not on the circle, the curve is called a trochoid: ... Some interesting properties of the cycloid:
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www.2dcurves.com/roulette/roulettec.html
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The involute of a cycloid is also a cycloid. cycloid_involute.gcf Both evolute and involute properties are easily proved by a direct application of the formula and simplify the result.
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xahlee.org/SpecialPlaneCurves_dir/Cycloid_dir/cycloid.h...
xahlee.org/SpecialPlaneCurves_dir/Cycloid_dir/cycloid.html
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