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 .
Ancient Egypt [TK] http://en.wikipedia.org/wiki/Image:Kheops-Pyramid.jpg
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:
, n is even , n is odd where n >1. which can be expressed as:
Ancient Greece The Parthenon http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#arch
Maragha, Iran [PL] [PL] Medieval Islamic Architecture [RD]
Le Corbusier 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]
[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.