The golden ratio φ satisfies φ² = φ + 1. The plastic number ρ satisfies the analogous cubic: ρ³ = ρ + 1. Its only real root is ρ ≈ 1.32471. Dutch architect Hans van der Laan, who studied three-dimensional proportions, named it "the plastic number" in the 1920s.
Just as Fibonacci ratios converge to φ, the Padovan sequence 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21… where each term equals the sum two and three steps back: has ratios converging to ρ. The plastic number is the dominant eigenvalue of this 3-step recurrence.
ρ is the smallest Pisot-Vijayaraghavan number an algebraic integer whose conjugate roots both lie strictly inside the unit circle. These numbers have special properties in Fourier analysis, tiling theory, and quasi-crystal structure.