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plastic constant
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(Definition)
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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.
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"plastic constant" is owned by PrimeFan. [ owner history (1) ]
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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
There are 5 references to this entry.
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 3007 times total.
Classification:
| AMS MSC: | 11B39 (Number theory :: Sequences and sets :: Fibonacci and Lucas numbers and polynomials and generalizations) |
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Pending Errata and Addenda
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