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# 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.

Synonym:

plastic number, silver number, silver constant

Type of Math Object:

Definition

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Reference

## Mathematics Subject Classification

11B39*no label found*

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