2017•AIP conference proceedingsRequires access
The relationship between the sum of reciprocal golden section numbers and the Fibonacci numbers
Haiquan Fang, Huifeng Xue, Tiejun Zhou
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Abstract
The golden section sequence of points was defined, and we found that the logarithmic spiral, golden section sequence, and Fibonacci sequence exhibit a close relationship. We considered infinite sums derived from the reciprocals of the golden section numbers and Fibonacci numbers, and infinite sums derived from the reciprocals of the square of the golden section numbers and Fibonacci numbers. Applying the floor function to the reciprocals of these sums, we determined that they are equal to each other.