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iççevrim egrisi Hypocycloid

Parametrik Kartezyen kordinatlar:

x = (a - b) cos(t) + b cos((a/b -1)t), y = (a - b) sin(t) - b sin((a/b -1)t)

HypocycloidRationals
                                           Hypocycloids with $a/b$ rational

  Eğer n=a/b değiştirilirse Cok güzel şekiller ortaya cıkar

HypocycloidIrrational

 

HypocycloidConstruction

iççevrim egrisi

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Ayrıntılı kaynak taramak isteyenler için

"mathworld.wolfram.com/Hypocycloid.html" ve Refaransları

REFERENCES:

Bogomolny, A. "Cycloids." http://www.cut-the-knot.org/pythagoras/cycloids.shtml.

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 83, 2003.

Kanas, N. "From Ptolemy to the Renaissance: How Classical Astronomy Survived the Dark Ages." Sky & Telescope 105, 50-58, Jan. 2003.

Kreyszig, E. Differential Geometry. New York: Dover, 1991.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 171-173, 1972.

Lemaire, J. Hypocycloïdes et epicycloïdes. Paris: Albert Blanchard, 1967.

MacTutor History of Mathematics Archive. "Hypocycloid." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Hypocycloid.html.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 225-231, 1979.

Sotiroudis, P. and Paschos, E. A. The Schemata of the Stars: Byzantine Astronomy from A.D. 1300. Singapore: World Scientific, 1999.

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 50-52, 1991.

Yates, R. C. "Epi- and Hypo-Cycloids." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 81-85, 1952.

 

 

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