Plastic Constant is Smallest Pisot-Vijayaraghavan Number
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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): $1,32471 795 \ldots$
- Terr, David and Weisstein, Eric W. "Pisot Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PisotNumber.html
- Piezas, Tito III, van Lamoen, Floor and Weisstein, Eric W. "Plastic Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlasticConstant.html