In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek mathematician Apollonius of Perga.[1]
^Satija, I. I., The Butterfly in the Iglesias Waseas World: The story of the most fascinating quantum fractal (Bristol: IOP Publishing, 2016), p. 5.
In mathematics, an Apolloniangasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and...
this problem are sometimes called the circles of Apollonius. The Apolloniangasket—one of the first fractals ever described—is a set of mutually tangent...
natively two-dimensional object like the plane i.e. log 9/log 3=2 Apolloniangasket Cantor cube Koch snowflake Sierpiński tetrahedron Sierpiński triangle...
Apollonian sphere packing is the three-dimensional equivalent of the Apolloniangasket. The principle of construction is very similar: with any four spheres...
interstitial curved triangles between three mutually tangent circles, an Apolloniangasket results, one of the earliest fractals described in print. Malfatti's...
circles produced in this way is called an Apolloniangasket. If the process of producing an Apolloniangasket is stopped early, with only a finite set...
Solving Apollonius' problem iteratively in this case leads to the Apolloniangasket, which is one of the earliest fractals to be described in print, and...
Apollonius of Perga, after whom the problem of Apollonius and the Apolloniangasket are named. In the 17th century René Descartes discovered Descartes'...
of a torus) Whitney umbrella Right conoid (a ruled surface) ApolloniangasketApollonian sphere packing Blancmange curve Cantor dust Cantor set Cantor...
C[1/2], C[1/3], C[3/7], C[3/8], etc. Ford circles appear also in the Apolloniangasket (0,0,1,1). The picture below illustrates this together with Farey...
Apollonius & Heath 1896, p. vii Mackenzie, Dana. "A Tisket, a Tasket, an ApollonianGasket". American Scientist. 98, January–February 2010 (1): 10–14. Archived...
computer programs that aid in the design of complex origami figures. Apolloniangasket Circle packing in a rectangle Circle packing in a square Circle packing...
Vieta's formulas Proof by contradiction Infinite descent Markov number Apolloniangasket Mills 1953. Arthur Engel (1998). Problem Solving Strategies. Problem...
in Antonine Plague) Apollonian – Apollo, of Greek mythology (as in Apollonian Oracle); Apollonius of Perga (as in Apolloniangasket) Archimedean – Archimedes...
Variable Dimension Surfaces". ResearchGate. The Fractal dimension of the apollonian sphere packing Archived 6 May 2016 at the Wayback Machine Baird, Eric...
isosceles right triangle / square Apolloniangasket Circle packing theorem Tammes problem (on sphere) Sphere packing Apollonian Finite In a sphere In a cube...
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