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Fibonacci Numbers in Architecture

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

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  1. Fibonacci Numbers in Architecture Emily Cookson

  2. Contents • Introduction • Alleged Golden Architecture • Ancient Egypt • Ancient Greece • Medieval Islamic Architecture • Golden Architecture • Le Corbusier • Fibonacci Spirals • Conclusion

  3. 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 .

  4. Ancient Egypt [TK] http://en.wikipedia.org/wiki/Image:Kheops-Pyramid.jpg

  5. 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:

  6. , n is even , n is odd where n >1. which can be expressed as:

  7. Ancient Greece The Parthenon http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#arch

  8. Maragha, Iran [PL] [PL] Medieval Islamic Architecture [RD]

  9. Le Corbusier The Modulor system is based on a six-foot (183cm) man. 183cm Chandigarh, India 113cm [TK] [KF]

  10. 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]

  11. [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

  12. 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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