Pentagon and the Golden Ratio

Pentagon and the Golden Ratio

The ancient Greek mathematicians began research on this, what we call today the ‘golden ratio’ because of his frequent presence in geometry. The division line in the "golden way” (the golden ratio) is a significant weight of symmetrical geometry pentagrams and pentagons. Greeks usually attributed to Pythagoras discovery of this relationship or his disciples. Pentagram inscribed equilateral with Pentagon was a symbol of the Pythagoreans.

Golden ratio is not only rectangles but keeping the ratio of 1.61 which plays an important role in 

the geometry of the pentagram where all portions intersect each other in the golden ratio. Also, 

the ratioof the shorter segment to the segment bounded by two intersecting edges (side of the pentagon

inside the pentagram) is φ, as shown illustration below.

Pentagram

Pentagram is coloured to distinguish his segments 

of different lengths. All four lengths are do himself

in the Golden Ratio. Pentagram contains ten

isosceles triangles: Five acute-angled and five 

obtuse. In all them ratio of the longer side to 

shorter side is φ. Acute-angled triangles are golden
triangles, obtuse are gold 'gnomons'.

A regular pentagon with an inscribed pentagram.

The following ratios of the lengths on the lines segments shown in the figure are equal to the golden ratio.The ‘ratio’ has become known as the golden ratio or golden section and can be found in many places in maths, architecture, art and design. Ratio of 1.61 can be used also with circles, for example, as itdid in Pepsi logo.

REFERENCES

Abrohms, Alison. Literature-Based Math Activities. 1992. New York: Scholastic Inc.

B. Burns, Marilyn. The Greedy Triangle. 1975. New York: Scholastic Inc.

C. Hickey, Mary. Big Book of Small Quilts. 1997. Oxmoor House, Inc. and Leisure Arts.