Practical Electron Microscopy and Database

Chapter/Index: Introduction | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Appendix

Golden Mean/Golden Ratio and Quasicrystals

Quasiperiodicity in quasicrystals may exist in 1-, 2-, or 3-dimensions of physical spaces and is related to special irrational numbers such as the golden mean ≈ 1.6180339887 that is related to five-fold symmetry through the relation . Here, τ is the interesting irrational number that has the worst approximation by a truncated continued fraction,           ------------------------------ [1445]