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.

单词	PlasticConstant
释义	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.
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