THE Golden Ratio

Razielle D., Jee Woo P., Danielle S., Alice C.

do these Images look familiar?

They all have one thing in common...

They all have one thing in common

The Golden Ratio

Also known as

Seems to be found EVERYWHERE...

THE GOLDEN MEAN,

THE GOLDEN NUMBER,

THE GOLDEN PROPORTION,

THE DIVINE PROPORTION,

THE DIVINE SECTION,

 

THE GOLDEN NUMBER,

 

 

 

 

THE DIVINE NUMBER.

What is The Golden ratio?

  • An irrational number

  • PHI (φ)=1.61803398874989484820...

  • The ratio of two numbers is a:a+b

Relationship with

the Fibonacci Sequence

Relationship of

the Fibonacci Sequence with the pascal triangle

    In summary: it is

  • a sequence of numbers created by adding the two numbers before it

  • 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

Relationship with

the Fibonacci Sequence

            Relationship:

  • take two successive Fibonacci numbers

  • ratio them (ex. 1/2, 2/3, 3/5, 5/8, 8/13...)

  • the bigger the number, the closer it gets to the Golden Ratio

that have the golden ratio

golden ratio shapes

Isosceles Triangle

  • the ratio a:b is equivalent to the golden ratio

  • bisecting an isosceles triangle made with 36° and 72° from the larger angle will get another isosceles triangle

   Isosceles Triangle

  • if the process continues, a spiral will form with an infinite amount of isosceles triangles

Golden Ratio Pentagram

  • contains five golden triangles

  • made by joining two non-adjacent corners to the central pentagon

  1. Construct a simple square

  2. Draw a line from the midpoint of one side of the square to an opposite corner

  3. Use that line as the radius to draw an arc that defines the height of the rectangle

  4. Complete the golden rectangle

Golden Ratio rectangle

TRY IT YOURSELF

The Golden Ratio is found in your daily life too

Other examples of Golden Ratio in life

The Golden Ratio

By Alice

The Golden Ratio

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