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## PowerPoint Slideshow about 'Fibonacci Numbers in Architecture' - ivanbritt

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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

- where , and ;
- ;
- The golden ratio is the ratio τ:1;
- Two measurements a and b, a>b, are in the golden ratio if .

Example from the Rhind papyrus:

from series

We can see that

;

from series

from series

from table

from table

Egyptian FractionsRatios of consecutive Fibonacci numbers using Egyptian mathematics:

Ancient Greece

The Parthenon

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

Le Corbusier

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

183cm

Chandigarh, India

113cm

[TK]

[KF]

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

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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