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The Apollonian Packing of Circles

✍ Scribed by Hirst, K. E.

Book ID: 120098666
Publisher: Oxford University Press
Year: 1967
Tongue: English
Weight: 250 KB
Volume: s1-42
Category: Article
ISSN: 0024-6107
DOI: 10.1112/jlms/s1-42.1.281

No coin nor oath required. For personal study only.

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✍ Edward Kasner and Fred Supnick 📂 Article 📅 1943 🏛 National Academy of Sciences 🌐 English ⚖ 271 KB

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Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

✍ Ronald L. Graham; Jeffrey C. Lagarias; Colin L. Mallows; Allan R. Wilks; Catheri 📂 Article 📅 2005 🏛 Springer 🌐 English ⚖ 427 KB

The spectral geometry of the apollonian

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✍ Robert Brooks 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 456 KB

Now let E be a fixed constant, and let x be an arbitrary point in supp(T) lying in this copy of Pick. As in [3], it follows from bounded mean curvature that there is a uniform lower bound for the area of an &-ball in T about x. This &-ball may meet at most a fixed number of copies of pick. Hence we