Quit Ratio Golden Ratio Fibonacci Quit Ratio Ratio

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Ratio Golden Ratio Fibonacci Quit

Ratio • Ratio is a way of showing the connection between two or more numbers. • A ratio can be written as a fraction, a decimal or as numbers with : between them. Quit

There are 30 students in a class; 18 are girls and 12 are boys. Express this as a ratio. • The ratio of girls to boys is: 18 : 12 or • 3 : 2 (simplifying) or 3 • –– (fraction) or 2 • 1· 5 (decimal) Quit

The Golden Ratio • At least since the Renaissance, many artists and architects have proportioned their works to approximate the Golden Ratio, believing this proportion to be aesthetically pleasing. • Leonardo da Vinci’s drawings of the human body emphasised its proportion. Quit

The Golden Ratio t b Quit

The Golden Ratio l Quit w

The Golden Ratio • This Golden Ratio has many unusual properties. We will take the number as 1· 618. • Remember, this is an approximation. The number is irrational. 1 ––––– = 0· 618 1· 618 Quit

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Fibonacci • Fibonacci, an Italian mathematician, developed a famous series in the thirteenth century. • Start with 1, 1. • Every number is calculated by adding the two previous numbers together. Quit

Fibonacci Series Quit 1 1 2 3 5 8

Golden Ratio • Compute the ratio of Fibonacci numbers: 2÷ 1= 2 3 ÷ 2 = 1· 5 5 ÷ 3 = 1· 666… 8 ÷ 5 = 1· 6 13 ÷ 8 = 1· 625 21 ÷ 13 = 1· 615… Quit

Fibonacci in Nature Quit

Spirals 13 21 8 Quit 2 3 1 1 5

Spirals Quit

Golden Ratio in Nature Quit

Golden Ratio in Architecture Great Wall of China Quit Parthenon, Greece

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