-1 = 1 F-2 = -1 F-3 = 2 F-4 = -3 provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles where each triangle has one 90° angle one 45° angle and one 36° angle." />
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Negafibonacci Numbers and the Hyperbolic Plane

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Abstract:

All integers can be represented uniquely as a sum of zero or more "negative" Fibonacci numbers F-1 = 1, F-2 = -1, F-3 = 2, F-4 = -3, provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles, where each triangle has one 90° angle, one 45° angle, and one 36° angle.
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Knuth, Donald. "Negafibonacci Numbers and the Hyperbolic Plane" Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA, <Not Available>. 2013-12-15 <http://citation.allacademic.com/meta/p206842_index.html>

APA Citation:

Knuth, D. "Negafibonacci Numbers and the Hyperbolic Plane" Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA <Not Available>. 2013-12-15 from http://citation.allacademic.com/meta/p206842_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: All integers can be represented uniquely as a sum of zero or more "negative" Fibonacci numbers F-1 = 1, F-2 = -1, F-3 = 2, F-4 = -3, provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles, where each triangle has one 90° angle, one 45° angle, and one 36° angle.

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