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The Golden Ratio

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Modern Art Uses the Golden Ratio ... Excursions in Modern Mathematics by Peter. Tannenbaum & Robert Arnold ... The Golden Ratio in Art s were taken from ... – PowerPoint PPT presentation

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Title: The Golden Ratio


1
The Golden Ratio
  • Marie Bruley
  • Math 21-Merced College

2
What is the Golden Ratio?
  • Phi
  • F

3
This is an approximation of its decimal expansion!
  • F

4
The Golden Ratio In Art
  • Throughout the centuries, artists and
    musicians - pursuing aesthetics - have turned to
    natures own tactics and emulated the golden ratio
    in their own creations. There is evidence of this
    from ancient times.

5
The Parthenon
6
The Parthenons Dimensions is the Golden Rectangle
7
The Floor Plan of the Parthenon
8
The Pyramids at Giza
9
The Use of Phi in the Pyramids
10
Michelangelos Use of the Golden Ratio
11
Raphaels Use of the Golden Ratio
  • Raphael's Crucifixion ... is another well-known
    example. The principal figures outline a golden
    triangle ...

12
Other Art
  • Norham Castle at Sunrise
  • The English romantic artistic Joseph Mallord
    William Turner (1775-1851) is admired for his use
    of color and light.   Norham Castle at Sunrise
  • Of particular interest are the geometric
    similarities in his various canvases, with their
    obvious golden subdivisions.

13
Modern Art Uses the Golden Ratio
  • The more recent search for a grammar of art
    inevitably led to the use of the golden section
    in abstract art. La Parade, painted in the
    characteristic multi-dotted style of the French
    neo-impressionist Seurat (1859-1891), contains
    numerous examples of golden proportions.

14
La Parade-By Seurat
15
Bathers-By Seurat
16
The Golden Ratio in Modern Architecture
  • The 20th Century architect Le Corbusier
    (1887-1965)
  • He used the Golden Ratio in his architecture
  • He believed that humans are comforted by
    mathematics.

17
Finding the Golden Ratio Using Fibonacci numbers
18
The Ratios of Fibonaccis leads to
19
Fibonacci Numbers Method Continued
  • This leads to solving

20
The Golden Ratio
x units 1 unit
R S T
21
The Golden Rectangle
Historical Note The Golden Ratio is also called
the Divine Proportion.
22
The Golden Triangle
Again, we have
36º
x x
1 unit
23
(No Transcript)
24
Websites Regarding the Golden Ratio
  • http//ccins.camosun.bc.ca/jbritton/goldslide/jbg
    oldslide.htm
  • http//mathworld.wolfram.com/GoldenRatio.html
  • http//students.bath.ac.uk/ma1caab/art.html
  • http//www.geocities.com/CapeCanaveral/Station/822
    8/

http//www.geocities.com/CapeCanaveral/Station/822
8/
25
Acknowledgements!
  • Textbooks consulted were
  • Excursions in Modern Mathematics by Peter
    Tannenbaum Robert Arnold
  • The slides for computing the Golden Ratio were
    taken from Marguerite Smiths presentation
    Fibonacci Numbers and the Golden Mean
  • The Golden Ratio in Art slides were taken from
    the website http//ccins.camosun.bc.ca/jbritton
    /goldslide/jbgoldslide.htm
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