The Interesting Golden Ratio

A Simple Mathematical Approach

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book The Interesting Golden Ratio by Vincent Siu, Partridge Publishing Singapore
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Author: Vincent Siu ISBN: 9781482855432
Publisher: Partridge Publishing Singapore Publication: February 11, 2016
Imprint: Partridge Publishing Singapore Language: English
Author: Vincent Siu
ISBN: 9781482855432
Publisher: Partridge Publishing Singapore
Publication: February 11, 2016
Imprint: Partridge Publishing Singapore
Language: English

This book uses simple geometry, trigonometry and algebra to explain how to construct and calculate the golden ratio. Starting from Euclids propositions in The Elements, the golden ratio and its related geometry such as the pentagon, pentagram and Vesica Piscis are constructed and determined graphically. Then the value of the ratio is solved by quadratic equations, and depending on the initial assumptions, two values are found. It is proposed that the ratio can be obtained easily by applying the Pythagoras theorem. Common terms like golden triangle, golden rhombus, golden spiral and golden angle are deduced and explained. The connections between the golden ratio and Fibonacci numbers, continued fractions, fractals, chaos and tiling are also introduced. The conclusion is that it is mathematics and not the golden ratio that is fascinating.

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This book uses simple geometry, trigonometry and algebra to explain how to construct and calculate the golden ratio. Starting from Euclids propositions in The Elements, the golden ratio and its related geometry such as the pentagon, pentagram and Vesica Piscis are constructed and determined graphically. Then the value of the ratio is solved by quadratic equations, and depending on the initial assumptions, two values are found. It is proposed that the ratio can be obtained easily by applying the Pythagoras theorem. Common terms like golden triangle, golden rhombus, golden spiral and golden angle are deduced and explained. The connections between the golden ratio and Fibonacci numbers, continued fractions, fractals, chaos and tiling are also introduced. The conclusion is that it is mathematics and not the golden ratio that is fascinating.

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