Quit

Quit

Ratio

Golden Ratio

Fibonacci

Quit

RatioRatio

• 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

• 1·5 (decimal)

32––• (fraction) or

Quit

The Golden RatioThe 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

b

t

The Golden RatioThe Golden Ratio

Quitw

l

The Golden RatioThe Golden Ratio

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 RatioThe Golden Ratio

11·618–––––= 0·618

Quit

Quit

FibonacciFibonacci

• 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

11235

8

Fibonacci SeriesFibonacci Series

Quit

• Compute the ratio of Fibonacci numbers:

2 ÷ 1 =

3 ÷ 2 =

5 ÷ 3 =

8 ÷ 5 =

13 ÷ 8 =

21 ÷ 13 =

Golden RatioGolden Ratio

21·5

1·666…

1·6

1·625

1·615…

Quit

Fibonacci in NatureFibonacci in Nature

Quit

21

SpiralsSpirals

1 12 3

58

13

Quit

SpiralsSpirals

Quit

Golden Ratio in NatureGolden Ratio in Nature

Quit

Great Wall of ChinaParthenon, Greece

Golden Ratio in ArchitectureGolden Ratio in Architecture

Yes No

Do you want to end show?