2. Quit

3. Ratio Golden Ratio Fibonacci

4. QuitRatio 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.

5. 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 1·5 (decimal) 3232 –– (fraction) or

6. 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.

7. Quit b t The Golden Ratio

8. Quit w l The Golden Ratio

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

10. Quit

11. 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.

12. Quit 1 1 2 3 5 8 Fibonacci Series

13. Quit Compute the ratio of Fibonacci numbers: 2 ÷ 1 = 3 ÷ 2 = 5 ÷ 3 = 8 ÷ 5 = 13 ÷ 8 = 21 ÷ 13 = Golden Ratio 2 1·51·5 1·666… 1·6 1·625 1·615…

14. Quit Fibonacci in Nature

15. Quit 21 Spirals 11 2 3 5 8 13

16. QuitSpirals

17. Golden Ratio in Nature

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

19. YesNo Do you want to end show?