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plastic constant (Definition)

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}-... ...\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.



"plastic constant" is owned by Mravinci.
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Other names:  plastic number, silver number, silver constant
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Cross-references: approximation, Perrin sequence, Padovan sequence, term, calculate, real numbers, solution, equation
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This is version 5 of plastic constant, born on 2006-08-17, modified 2006-08-22.
Object id is 8264, canonical name is PlasticConstant.
Accessed 1632 times total.

Classification:
AMS MSC11B39 (Number theory :: Sequences and sets :: Fibonacci and Lucas numbers and polynomials and generalizations)

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