The Golden Section

The Golden Section reflects a ratio - the Golden or Divine Ratio - encountered everywhere throughout nature. In Antique architecture it was used to determine the most 'pleasing' proportion within, for instance, the façade of a temple. Euclid has shown how to divide a line to obtain the Golden Section: 
|   a   |      b      |
where 
a : b = b  : (a + b)
which is true for a = 5 - 1 and b = 2. This ratio a/b yields a value of 0.6180339887499... called (phi, lowercase). This value relates to the so-called Golden Number, (capital Phi) which equals +1. The Golden Number is defined by: 
N2 = N + 1
which is true for N = and N = -. The value is approached by the ratio of successive numbers in Fibonacci's series (1,1,2,3,5,8,13,21,..).

The Golden Section recurs in Gothic architecture, although I don't think it is used as extensively as in Classical architecture. At present I'm still collecting examples of its usage during the Middle Ages. (Please send any suggestions to helfrich@xs4all.nl.)

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Nave at Reims, sections
The nave at Reims - possible Golden Sections.
Golden sections at Laon
Laon - Golden sections identified by Wilmink (Mijn Middeleeuwen, 1999). Also note the pentagon. 		Freiburg: Fibonacci numbers
Münster Church, Freiburg - Fibonacci numbers (ref. Snijders De Gulden Snede, 1969).

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