Plastic Constant is Smallest Pisot-Vijayaraghavan Number

From ProofWiki
Jump to navigation Jump to search


The plastic constant is the smallest Pisot-Vijayaraghavan number.


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.


  • 1944: R. SalemA Remarkable Class of Algebraic Numbers. Proof of a Conjecture of Vijayaraghavan (Duke Math. J. Vol. 11: pp. 103 – 108)
  • 1944: C.L. SiegelAlgebraic Numbers whose Conjugates lie in the Unit Circle (Duke Math. J. Vol. 11: pp. 597 – 602)