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Encyclopedia > Plastic constant

The plastic number (also known as the plastic constant) is the unique real solution of the equation

and has the value

which is approximately 1.324717957244746025960908854 (sequence A060006 in OEIS). The plastic number is also sometimes called the silver number, but that name is more commonly used for the silver ratio . The plastic number is the limiting ratio of successive terms of the Padovan sequence and the Perrin sequence, and bears the same relationship to these sequences as the golden ratio does to the Fibonacci sequence and the silver ratio does to the Pell numbers. The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ... The silver ratio is a mathematical constant. ... The Padovan sequence is the sequence of integers P(n) defined by the initial values and the recurrence relation The first few values of P(n) are 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 144, 151, 200. ... In mathematics, the Perrin pseudoprimes are derived from the Perrin series of numbers. ... The golden section is a line segment sectioned into two according to the golden ratio. ... In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ... The silver ratio is a mathematical constant. ... In mathematics, the Pell numbers and companion Pell numbers (Pell-Lucas numbers) are both sequences of integers. ...


The plastic number is also a solution of the following equations:

The plastic number is the lowest Pisot-Vijayaraghavan number. In mathematics, a Pisot-Vijayaraghavan number is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than 1 in absolute value. ...


References

  • Midhat J. GazalĂ©, Gnomon, 1999 Princeton University Press.

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