Page 18 - Module 1_Chapter 1_Mathematics in the Modern World

Mathematics in our World
8

The Golden Ratio

Two quantities are in the Golden

ratio if their ratio is the same of their

sum to the larger of the two quantities.

The Golden Ratio is the relationship

between numbers on the Fibonacci

sequence where plotting the

relationships on scales results in a

spiral shape.

In simple terms, golden ratio is

expressed as an equation, where a is

larger than b, (a + b) divided by a is The Golden Rectangle

equal to a divided by b, which is equal

to 1.618033987… and represented by a
The golden ratio is the limit of the ratios of
Greek character .
successive terms of the Fibonacci sequence

(or any Fibonacci-like sequence), as originally

shown by Johannes Kepler (1571–1630).

Golden ratio can also be deduced in an
The Fibonacci numbers can be
isosceles triangle. A set of Whirling Triangles
applied to the proportions of a rectangle
were able to draw a logarithmic spiral that will
called the Golden rectangle. Golden
converge at the intersection of the two lines.
Rectangle is known as one of the most

visually satisfying of all geometric forms

– hence, the appearance of the Golden
ratio in art. The Golden rectangle is also

related to the Golden spiral, which is
created by making adjacent squares of
The Golden Triangle
Fibonacci dimensions. A Fibonacci

spiral which approximates the golden
spiral, using Fibonacci sequence
square sizes up to 34.

ZANNIE I. GAMUYAO, MSM
Assistant Professor 1 UNIT 1.2 The Fibonacci Sequence
Department of Arts and Sciences