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Fibonacci Numbers in Architecture. Emily Cookson. Contents. Introduction Alleged Golden Architecture Ancient Egypt Ancient Greece Medieval Islamic Architecture Golden Architecture Le Corbusier Fibonacci Spirals Conclusion. Fibonacci Numbers and the Golden Ratio.

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Presentation Transcript
contents
Contents
  • Introduction
  • Alleged Golden Architecture
    • Ancient Egypt
    • Ancient Greece
    • Medieval Islamic Architecture
  • Golden Architecture
    • Le Corbusier
    • Fibonacci Spirals
  • Conclusion
fibonacci numbers and the golden ratio
Fibonacci Numbers and the Golden Ratio
  • where , and ;
  • ;
  • The golden ratio is the ratio τ:1;
  • Two measurements a and b, a>b, are in the golden ratio if .
ancient egypt
Ancient Egypt

[TK]

http://en.wikipedia.org/wiki/Image:Kheops-Pyramid.jpg

egyptian fractions

Example from the Rhind papyrus:

from series

We can see that

;

from series

from series

from table

from table

Egyptian Fractions

Ratios of consecutive Fibonacci numbers using Egyptian mathematics:

slide6

, n is even

, n is odd

where n >1.

which can be expressed as:

ancient greece
Ancient Greece

The Parthenon

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#arch

le corbusier
Le Corbusier

The Modulor system is based on a six-foot (183cm) man.

183cm

Chandigarh, India

113cm

[TK]

[KF]

le modulor

27 43 7086 113 140183 226

Le Modulor
  • séries rouge:
  • 4-6-10-16-27-43-70-113-183-296…;
  • séries bleue:
  • 13-20-33-53-86-140-226-366-592… .

[KF]

fibonacci spirals

[KF]

Fibonacci Spirals

The Spiral Café, Birmingham

Core Model, Eden Project

http://www.civictrust.org.uk/cta2006/awardpages/awardspiral.htm

http://www.cda.org.uk/arch/pages/Design_awards/cia12/Spiral%20Cafe/spiralcafe.htm

http://plus.maths.org/latestnews/may-aug06/bridges/Eden.jpg

conclusion
Conclusion
  • Claims that Fibonacci numbers and the golden ratio were used in architecture are difficult to prove without original documentary evidence;
  • Modern architects have been inspired by Fibonacci numbers and the golden ratio;
  • Do you find the golden ratio the most aesthetically pleasing ratio?

Acknowledgements: [KF] K Frampton, Le Corbusier, Thames & Hudson, 2001; [TK] T Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, Inc., 2001;

[RD] R A Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, 1997; [PL] Peter J. Lu, et al., Decagonal and quasi-crystalline tilings in medieval

Islamic architecture, Science 315, 1106 (2007); [SV] S Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Ellis Horwood Ltd, 1989.

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