The Golden Ratio: The Facts and the Myths by Hauser Francis

Author:Hauser, Francis [Hauser, Francis]
Language: eng
Format: epub
Publisher: Createspace Independent Publishers
Published: 2015-10-20T21:00:00+00:00

Figure 14: The First Ten Fibonacci Numbers

To Fibonacci, this was nothing more than an example problem in his textbook. In fact, because it was a twelve-month rabbit-propagation problem, only the first twelve numbers appear in Liber Abaci.

Around 1600, Kepler (of solar system fame) was studying Euclid’s The Elements, Pacioli’s The Divine Proportion, and Fibonacci’s Liber Abaci. For his reasons, Kepler computed the ratio of successive Fibonacci numbers. These are plotted in figure 15.

Figure 15: Ratio of Successive Fibonacci Numbers

Kepler saw that as the numbers get larger, this ratio approaches the value of 1.618. This is the value of Φ. And Kepler regarded Φ as the “jewel of geometry.” Again Φ is associated with a famous person, and the myth grows. But let’s study this a little bit.

Around 1800, Edouard Lucas, a prominent French mathematician, published another famous series of numbers. This bears his name. His series uses the Fibonacci equation, but with different starting values (F1 = 1 and F2 = 3). This series is plotted in the following figure.

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