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Ratio Golden Ratio Fibonacci

Ratio Golden Ratio Fibonacci. 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. 3 2. ––. (fraction) or. There are 30 students in a class; 18 are girls and 12 are boys.

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Ratio Golden Ratio Fibonacci

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  1. Ratio Golden Ratio Fibonacci

  2. 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.

  3. 3 2 –– • (fraction) or • 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 • 1·5 (decimal)

  4. 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.

  5. t b The Golden Ratio

  6. l w The Golden Ratio

  7. 1 1·618 ––––– = 0·618 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.

  8. 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.

  9. Fibonacci Series 1 1 2 3 5 8

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

  11. Fibonacci in Nature

  12. Spirals 13 21 8 2 3 1 1 5

  13. Spirals

  14. Golden Ratio in Nature

  15. Golden Ratio in Architecture Parthenon, Greece Great Wall of China

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