Silver ratio
| Rationality | irrational algebraic |
|---|---|
| Symbol | σ |
| Representations | |
| Decimal | 2.41421356237309504880... |
| Algebraic form | positive root of x2 = 2x + 1 |
| Continued fraction (linear) | [2;2,2,2,2,2,...] purely periodic infinite |
In mathematics, the silver ratio is a geometrical proportion with exact value 1 + √2, the positive solution of the equation x2 = 2x + 1.
The name silver ratio results from analogy with the golden ratio, the positive solution of the equation x2 = x + 1.
Although its name is recent, the silver ratio (or silver mean) has been studied since ancient times because of its connections to the square root of 2, almost-isosceles Pythagorean triples, square triangular numbers, Pell numbers, the octagon, and six polyhedra with octahedral symmetry.