TOPICS
Tribonacci Constant
The tribonacci constant is ratio to which adjacent tribonacci numbers tend, and is given by
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(1)
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 |  | ![1/3(1+RadicalBox[{19, -, 3, {sqrt(, 33, )}}, 3]+RadicalBox[{19, +, 3, {sqrt(, 33, )}}, 3])](https://mathworld.wolfram.com/images/equations/TribonacciConstant/Inline6.svg) |
(2)
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(3)
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(OEIS A058265).
The tribonacci constant satisfies the identities
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(4)
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(5)
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(6)
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(7)
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(P. Moses, pers. comm., Feb. 21, 2005).
The tribonacci constant is extremely prominent in the properties of the snub cube.
See also
Hard Hexagon Entropy Constant, Snub Cube, Tetranacci Constant, Tribonacci SequenceExplore with Wolfram|Alpha
References
Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 9, 2003.Pegg, E. Jr. "Shattering the Plane with Twelve New Substitution Tilings Using 2,
,
,
,
."
Mar. 7, 2019. https://blog.wolfram.com/2019/03/07/shattering-the-plane-with-twelve-new-substitution-tilings-using-2-phi-psi-chi-rho/.Sloane,
N. J. A. Sequence A058265 in "The
On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Tribonacci ConstantCite this as:
Weisstein, Eric W. "Tribonacci Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TribonacciConstant.html