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Apollonian
Apollonian, a. and n. (æpəˈləʊnɪən) [f. L. Apollōni-us, a. Gr. ἀπολλώνι-ος of Apollo; also pr. name + -ian] A. adj. 1. Pertaining to, resembling, or having the characteristics of Apollo, the sun-god of the Greeks and Romans, the patron of music and poetry.1663 Gerbier Counsel B vj a, To destroy the ... Oxford English Dictionary
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Apollonian network
from an Apollonian network produces a graph that is not an Apollonian network. Degeneracy In every subgraph of an Apollonian network, the most recently added vertex has degree at most three, so Apollonian networks have degeneracy wikipedia.org
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Apollonian network and 4 coloring Is there a connection between the Apollonian network and the four-color theorem? Are there any attempts to prove this theorem using the Apollonian network?
As Wikipedia's article on Apollonian networks mentions, " _Birkhoff (1930) is an early paper that uses a dual form of Apollonian networks, the planar maps Curiously, he does not cite Birkhoff's 1930 paper and does not use the name "Apollonian network".
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Apollonian and Dionysian
Truth being primordial pain, our existential being is determined by the Dionysian/Apollonian dialectic. Support mostly takes the form of grants, and the present methods of distributing grants unduly favor the Apollonian". wikipedia.org
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Apollonian gasket
See also Apollonian network, a graph derived from finite subsets of the Apollonian gasket Apollonian sphere packing, a three-dimensional generalization Interactive Apollonian Gasket Demonstration of an Apollonian gasket running on Java Dana Mackenzie. wikipedia.org
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What would you call Apollonian circles that are located within polygon Sorry, if this question is dumb, but: When you try to fill the circle with other circles - its called Apollonian circles, and there are resources...
It appears that it is called an Apollonian packing of the polygon.
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Apollonian circles
In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second Definition The Apollonian circles are defined in two different ways by a line segment denoted . wikipedia.org
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Integral Apollonian circle packing with unique curvatures I was wondering if it is possible to construct an Apollonian gasket where every circle has a unique integer curvature. Take for instance the following gasket,...
Take a look at the values you're getting, mod 12. All the values are $2, 3, 6, 11$ (mod 12). If you look at more of these gaskets, you'll find that they always can only hit 4 values, mod 12. That severely limits the possible spread of values. From there, you can use the pigeonhole principle on the p...
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Apollonian sphere packing
Apollonian sphere packing is the three-dimensional equivalent of the Apollonian gasket. Software for generating and visualization of the apollonian sphere packing: ApolFrac. References Fractals Hyperbolic geometry Packing problems wikipedia.org
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integral apollonian sphere packing Can a sequence of cotangent spheres be packed inside a sphere so that the reciprocals of all of the radii are integers, like the integral apollonian circle packings on <
Yes - see the "bowl of integers". And if you want to go to higher dimensions, there's a paper of Graham et al.
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Circles of Apollonius
The Apollonian circles are two families of mutually orthogonal circles. arbitrarily finely, forming an Apollonian gasket, also known as a Leibniz packing or an Apollonian packing. wikipedia.org
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Number of circles in Apollonian fractals I am studying Apollonian fractals. According to this web page, number of circles in Apollonian fractals is $2+3^{(n+1)}$, which n means stage. How can I prove it? I guess the...
You start with three circles initially, that are not going to be counted initially. Then you add the inner and outer tangent circles : $a_0=2$. From then on every circle from stage $n$ is going to be surrounded by three new circles at stage $n+1$, therefore the amount of circles added at stage $n+1$...
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apollonian net in Chinese - apollonian net meaning in Chinese ...
apollonian net in Chinese : [网络] 阿波罗尼亚网 …. click for more detailed Chinese translation, meaning, pronunciation and example sentences.
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The Rape of The Lock: the Myth of Dionysian and Apollonian Womanhood
Alexander Pope rewrites a western myth by acquiring mythological stories about various human experiences from the Greeks, Romans, and Christians, but he reflects this mythopoeic world in The Rape of the Lock, embodying the femininity of Apollonian Belinda and Dionysian Clarissa.
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Why is the Apollonian Gasket composed of infinitely many circles? This famously known fractal has infinitely many circles, however I find it hard to find a rigid proof that confirms how or why this fractal is composed...
Every "gap" at any stage of the gasket is a region surrounded by three tangent circles. This is true at the start, as you can tell; it's also true every time you insert another circle. Every such concave region surrounded by three tangent circles has two places you can put a circle such that it's ta...
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