Exploring the World of Mathematics by Tiner John Hudson

Author:Tiner, John Hudson [Tiner, John Hudson]
Language: eng
Format: epub
Tags: Religion / Christian Education / General, Mathematics / General
ISBN: 9781614581550
Publisher: Master Books
Published: 2004-05-31T00:00:00+00:00

Suppose you start making fractions of pairs of Fibonacci numbers 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13 and so on. Written as decimal numbers, the fractions are 1.000, 2.000, 1.500, 1.667, 1.600, 1.625, 1.615. The pattern gets closer and closer to 1.618, which is the approximate decimal value for the Golden Ratio. The fraction formed by Fibonacci numbers 89 and 144, 144/89, have a decimal value of 1.618, which is the same as the Golden Ratio to three decimal places.

Look at the outer perimeter of the rectangle made from the squares. It has pleasing proportions of the golden rectangle.

Suppose arcs of circles are drawn diagonally from one corner of the one unit square to the other corner and then into the next square. The result is a beautiful spiral called a Fibonacci spiral. See figure 8-4.

Figure 8-4

Arcs of circles in the Fibonacci squares form a Fibonacci spiral.

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