Abstract
Basic properties of the golden ratio geometric problems in two dimensions geometric problems in three dimensions Fibonacci numbers Lucas numbers and generalized Fibonacci numbers continued fractions and rational approximants generalized Fibonacci representation theorems optimal spacing and search algorithms commensurate and incommensurate projections Penrose tilings quasicrystallography biological applications construction of the regular pentagon the first 100 Fibonacci and Lucas numbers relationships involving Fibonacci and Lucas numbers.
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