Plastic Constant is Smallest Pisot-Vijayaraghavan Number

Theorem

The plastic constant is the smallest Pisot-Vijayaraghavan number.


Proof


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Historical Note

The plastic constant was identified by Raphaël Salem in $1944$ as being the smallest known Pisot-Vijayaraghavan number.

Later that year Carl Ludwig Siegel showed that it was also the smallest possible.


Sources

  • 1944: R. Salem: A Remarkable Class of Algebraic Numbers. Proof of a Conjecture of Vijayaraghavan (Duke Math. J. Vol. 11: pp. 103 – 108)
  • 1944: C.L. Siegel: Algebraic Numbers whose Conjugates lie in the Unit Circle (Duke Math. J. Vol. 11: pp. 597 – 602)
  • 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,32471 795 \ldots$
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