Plastic ratio
A spiral of rectangles in the plastic ratio. | |
| Rationality | irrational algebraic |
|---|---|
| Symbol | ρ |
| Representations | |
| Decimal | 1.32471795724474602596... |
| Algebraic form | real root of x3 = x + 1 |
| Continued fraction (linear) | [1;3,12,1,1,3,2,3,2,4,2,141,80,...] not periodic infinite |
In mathematics, the plastic ratio is a geometrical proportion, given by the unique real solution of the equation x3 = x + 1. Its decimal expansion begins with 1.324717957244746... (sequence A060006 in the OEIS).
The adjective plastic does not refer to the artificial material, but to the formative and sculptural qualities of this ratio, as in plastic arts.