Blog Archives

The silver ratio

Most people have heard of the golden ratio, but have you ever heard of the silver ratio? I only heard of it this week. The golden ratio can be expressed by a continued fraction in which all coefficients equal 1.

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Breastfeeding, the golden ratio, and rational approximation

Gil Kalai’s blog featured a guest post the other day about breastfeeding twins. The post commented in passing that φ, the golden ratio, is the number hardest to approximate by rationals. What could this possibly have to do with breastfeeding?

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Golden ratio and special angles

The golden ratio comes up in unexpected places. This post will show how the sines and cosines of some special angles can be expressed in terms of the golden ratio and its complement.

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Connecting Fibonacci and geometric sequences

Here’s a quick demonstration of a connection between the Fibonacci sequence and geometric sequences. The famous Fibonacci sequence starts out 1, 1, 2, 3, 5, 8, 13 … The first two terms are both 1, then each subsequent terms is

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Fibonacci numbers at work

Today I needed to use Fibonacci numbers to solve a problem at work. Fibonacci numbers are great fun, but I don’t recall needing them in an applied problem before. I needed to compute a series of integrals of the form f(x, y)

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