# plastic constant

Given the equation $P^{3}=P+1$, solve for $P$. The only solution in real numbers is $P=\sqrt[3]{\frac{1}{2}+\frac{1}{6}\sqrt{\frac{23}{3}}}+\sqrt[3]{\frac{1}{2}-% \frac{1}{6}\sqrt{\frac{23}{3}}}=\frac{\sqrt[3]{12(9+\sqrt{69})}+\sqrt[3]{12(9-% \sqrt{69})}}{6}\approx 1.3247179572447$, and $P$ is the plastic constant, also known as the silver number.

Another way to calculate the plastic constant is ${{P(n)}\over{P(n-1)}}$, where $P(n)$ is the $n^{th}$ term of either the Padovan sequence or the Perrin sequence. For about $n>20$ the approximation is adequate for all practical purposes.

Title plastic constant PlasticConstant 2013-03-22 16:10:39 2013-03-22 16:10:39 PrimeFan (13766) PrimeFan (13766) 8 PrimeFan (13766) Definition msc 11B39 plastic number silver number silver constant