# 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 $\frac{P(n)}{P(n-1)}$, 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 |
---|---|

Canonical name | PlasticConstant |

Date of creation | 2013-03-22 16:10:39 |

Last modified on | 2013-03-22 16:10:39 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 8 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11B39 |

Synonym | plastic number |

Synonym | silver number |

Synonym | silver constant |