Also known as The Golden Mean The Golden Section.

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Presentation transcript:

also known as The Golden Mean The Golden Section

The square on the hypotenuse is equal to the sum of the squares on the other two sides = = 25

11 2

Each number is the sum of the 2 previous numbers

2

How many golden triangles can you see? D A B C E

AB = 5 AC = 4 BC = 3 PQ BP = φ= φ

AB = BC = CA AL = BL AM = CM

When 3 equal circles touch each other in sequence, and a larger semicircle, the ratio of the radius of the semicircle to the diameter of the small circles is φ.

The area of an annulus defined by the radii, a and b (b < a) is equal to the area of an ellipse with major and minor axis radii equal to a and b, respectively, when a/b = φ a bb a

Two examples of flower heads containing multiple seeds in spiral arrays

21 clockwise spirals 13 anticlockwise spirals

Storms and galaxies are often spirals but are they Golden Ratio spirals?

The Golden End