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Superplastic Ratio

The name superplastic ratio is used in this work for the unique positive real root chi of the quartic equation

x^4=x^3+1.

It has numeric value

chi=1.380277569097614115...

(OEIS A086106) and is the second smallest Pisot number (Siegel 1944). Pegg (2019) used the symbol chi for the constant in similar triangle dissections and substitution tilings.

The superplastic ratio is the n=3 self-summing ratio and appears as beta_3 in the family studied by Baker (2017).

See also

Golden Ratio, Pisot Number, Plastic Constant, Self-Summing Ratio, Substitution Tiling, Supergolden Ratio

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References

Baker, S. "Exceptional Digit Frequencies and Expansions in Non-Integer Bases." 28 Nov 2017. https://arxiv.org/abs/1711.10397.Pegg, E. Jr. "Shattering the Plane with Twelve New Substitution Tilings Using 2, phi, psi, chi, rho." Mar. 7, 2019. https://blog.wolfram.com/2019/03/07/shattering-the-plane-with-twelve-new-substitution-tilings-using-2-phi-psi-chi-rho/.Siegel, C. L. "Algebraic Numbers Whose Conjugates Lie in the Unit Circle." Duke Math. J. 11, 597-602, 1944.Sloane, N. J. A. Sequence A086106 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Superplastic Ratio." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SuperplasticRatio.html

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