A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than 1 and of degree 2 or 3 is a Pisot number if its norm is equal to ± 1. The golden ratio ϕ (denoted θ_0 when considered as a Pisot number) is an example of a Pisot number since it has degree two and norm -1. The smallest Pisot number is given by the positive root θ_1 = 1.32472... (OEIS A060006) of x^3 - x - 1 = 0, known as the plastic constant. This number was identified as the smallest known by Salem, and proved to be the smallest possible by Siegel.
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