The Golden Ratio | Homework Help

The Golden Ratio

Tags: algebra, divine proportion, divine section, extreme and mean ratio, golden, golden cut, golden mean, golden number, golden proportion, golden ratio, golden section, Math, mean of Phidias, medial section, proportion, ratio

Post Date

September 25, 2009

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An Introduction to the Golden Ratio

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Description

A detailed tutorial on the golden ratio. Step by step tutorial including several examples of the golden ratio for reference.

Overview

The golden ratio is a ratio in mathematics and the arts that is closely related to the Fibonacci numbers. It is said that two quantities are in the g0lden ratio if the ratio of the sum of the quantities to the larger number equals the ratio of the larger number to the smaller number. The algebraic expression of this is:

$\frac{a+b}{a} = \frac{a}{b} = \varphi\,.$

This equation has a unique solution, which is:

$\varphi = \frac{1+\sqrt{5}}{2}\approx 1.61803\,39887\ldots\,$

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