FIDIAS

He is deemed as the

creator and developer

of the idea for the first

time

GOLDEN RATIO

PARTHENON

http://upload.wikimedia.org/wikipedia/commons/5/51/Kien_truc_symbol.JPG

"Study for Phidias in 'The Apotheosis of Homer' by Ingres,

San Diego Museum of Art" by Wmpearl - Own work.

Licensed under Creative Commons Zero, Public Domain

Dedication via Wikimedia Commons -

http://commons.wikimedia.org/wiki/File:Study_for_Phidias_in

_%27The_Apotheosis_of_Homer%27_by_Ingres,_San_Dieg

o_Museum_of_Art.JPG#mediaviewer/File:Study_for_Phidias

_in_%27The_Apotheosis_of_Homer%27_by_Ingres,_San_Di

ego_Museum_of_Art.JPG

A B

CE

D

In every regular pentagon, the side AB is the Golden Ratio of the diagonal AD.

The shape brought about by the diagonals is a five point star or pentacle. In

the center of the pentacle there is a new pentagon upside down, where one

can draw again a pentacle. This process may last for good.

AD

AB1.618

F

EB

EF1.618

AB

AD0.618

EF

EB0.618

The Golden Ratio is found when we divide a line segment into two parts so

that:

the longer part divided by the shorter part

is also equal to

the whole length divided by the longer part

and the result of these divisions equals

1.618

AD

AB1.618

AD

AB AD-AB

AB

AD-AB= =

And, conversely:

the shorter part divided by the longer part

is also equal to

the longer part divided by the whole length

and the result of these divisions equals

0.618

AD

AB0.618

AD

AB AD-AB

AB

AD-AB= =

As a consequence:

Assuming AD=1

AB=0.618

and

AD-AB=0.382

With the help of a calculator, try to check all the ratios you learned in

the last two slides

AD

AB AD-AB

5

Number Five is related to human hands, protection and

salvation. It is also the quintessence, that is, which comes

after the four prime elements.

The Five-pointed star represents the devil

when put upside down

The Five-pointed star represents a human being

Many strongholds have a pentagonal shape. Do you know

any building in the USA related to this shape?

See page for author [Public domain], via Wikimedia CommonsBy Claudio.stanco (Own work) [CC-BY-SA-3.0

(http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia

Commons

ARCHITECTURAL EXAMPLES

Roger van der Weyden (1399/1400–1464) [Public domain undefined Public domain], undefined

ROGIER VAN DER

WEYDEN

THE DESCENT FROM THE

CROSS (1435)

"Diego Velázquez - The Surrender of Breda (Las Lanzas) - WGA24401" by Diego Velázquez - Web Gallery of Art: Image Info about artwork.

Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Diego_Vel%C3%A1zquez_-

_The_Surrender_of_Breda_(Las_Lanzas)_-_WGA24401.jpg#mediaviewer/File:Diego_Vel%C3%A1zquez_-

_The_Surrender_of_Breda_(Las_Lanzas)_-_WGA24401.jpg

X= 0.618 a-x=0.382

y b-y

a=1

b

The key becomes the most

relevant part in the picture

Point the compass on B and take radius AB. You will get C on the perpendicular to AB from B.

Draw the perpendicular bisector of BC to get M, middle point of BC

In order to better analyze the image, these are the main steps to find out the proportion in the

image

1

Point the compass on M and take radius MC. Join A to M and you will get P on the circle.

AP is the golden ratio of AB

2

Point the compass on A and take radius AP, that is, X. Draw the arch PQ and you will have

transferred X over AB. Finally, draw from Q a line perpendicular to AB, you can tell that this line, in

pink color, perfectly fits the first spear of the Spanish army. If you put QB from A, you will get the

whole distribution

3

El Greco [Public domain], via Wikimedia Commons

El Greco [Public domain], via Wikimedia Commons

0.6

18

0.6

18

0.3

82

0.3

82

GOLDEN RATIO IN NATURE

THE PINECONE AND THE GOLDEN SPIRAL

SEA STARS, VEGETABLES AND GALAXIES

AGRIMONY CARNATION VINCA

PETUNIA PETUNIA AQUILEGIA

FLOWERS

VEGETABLES GROW FOLLOWING A

GOLDEN SPIRAL LIKE MOVEMENT