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# Fibonacci Numbers in Architecture - PowerPoint PPT Presentation

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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### Fibonacci Numbers in Architecture

Emily Cookson

• Introduction

• Alleged Golden Architecture

• Ancient Egypt

• Ancient Greece

• Medieval Islamic Architecture

• Golden Architecture

• Le Corbusier

• Fibonacci Spirals

• Conclusion

• where , and ;

• ;

• The golden ratio is the ratio τ:1;

• Two measurements a and b, a>b, are in the golden ratio if .

[TK]

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

from series

We can see that

;

from series

from series

from table

from table

Egyptian Fractions

Ratios of consecutive Fibonacci numbers using Egyptian mathematics:

, n is even

, n is odd

where n >1.

which can be expressed as:

The Parthenon

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

[PL]

[PL]

Medieval Islamic Architecture

[RD]

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

183cm

Chandigarh, India

113cm

[TK]

[KF]

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

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

• 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.