Golden Ratio and Fibonacci Sequence in Pentagonal Constructions of Medieval Architecture

Golden Ratio and Fibonacci Sequence in Pentagonal Constructions of Medieval Architecture AbstractThe construction of the regular pentagon has always meant a difficult geometrical exercise for architects during the Middle Ages. As the correct drafting was forgotten after the Antiquity, several methods for its approximation had been invented in medieval times. As Golden Ratio appears between several parts of the regular pentagon, the role of the Fibonacci sequence in these approximate constructions is to be examined. The pentagonal drawing in the sketchbook of Villard de Honnecourt calls our attention to a possible way how medieval architects could have applied simple numerical ratios for getting angles they needed. The approximation of 72°, for instance, is likely to have been crucial for this pentagonal construction, as well as the approximation of Golden Ratio that could have been achieved by neighbouring pairs from Fibonacci’s sequence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png YBL Journal of Built Environment de Gruyter

Golden Ratio and Fibonacci Sequence in Pentagonal Constructions of Medieval Architecture

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Publisher
Sciendo
Copyright
© 2018 Krisztina Fehér, published by Sciendo
ISSN
2063-997X
eISSN
2064-2520
D.O.I.
10.2478/jbe-2018-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractThe construction of the regular pentagon has always meant a difficult geometrical exercise for architects during the Middle Ages. As the correct drafting was forgotten after the Antiquity, several methods for its approximation had been invented in medieval times. As Golden Ratio appears between several parts of the regular pentagon, the role of the Fibonacci sequence in these approximate constructions is to be examined. The pentagonal drawing in the sketchbook of Villard de Honnecourt calls our attention to a possible way how medieval architects could have applied simple numerical ratios for getting angles they needed. The approximation of 72°, for instance, is likely to have been crucial for this pentagonal construction, as well as the approximation of Golden Ratio that could have been achieved by neighbouring pairs from Fibonacci’s sequence.

Journal

YBL Journal of Built Environmentde Gruyter

Published: May 30, 2018

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