This article was taken from the May 2013 issue of Wired magazine. Be the first to read Wired's articles in print before they're posted online, and get your hands on loads of additional content by <span class="s1">subscribing online.
Want to build a cathedral? Know your proportions: geometry lay at the heart of medieval cathedral design. Far from having an academic understanding of mathematical principles, master masons had a purely practical knowledge of geometry, calculating the proportions of plans, profiles and façades with nothing more than a pair of compasses and a square. Malcolm Hislop, author of
How to Build a Cathedral (Bloomsbury, £24.99), explains how to construct proportionally perfect rectangles like a master.
The golden section
This most "beautiful" of proportions, 1:1.62, features in the columns of Durham Cathedral. Draw a square and a line between the midpoints of opposing sides, halving the square. Add a diagonal between two corners of one half. Put the compass at the midpoint of one side of the square and the pencil on an opposing corner. Draw an arch. Extend one side of the square to meet the arch and extend the square into a rectangle with this new length. The rectangle's length will be <span class="s3">1.62 times that of the base.
One to the square root of two
Draw a square. Add a diagonal line between two of its corners. The length of this line will be the radius of an arch that will determine the length of the rectangle. Place the point of the compass on one of the square's corners and the pencil on the opposite corner, and draw an arch around the square. Extend the length of one side of the square to meet the arch -- this is your rectangle's length, which will be 1.41 times that of the base. This is in the Portail Royale of Chartres Cathedral.
One to the square root of three
For this proportion, draw an equilateral triangle of any size. Draw a line from the centre of the base to the apex.
One half of the base equals the short side of the rectangle, and the perpendicular equals the long side. These proportions are in the profile of Milan Cathedral, ultimately derived from the equilateral triangle. Drawing rectangles that showed these proportions was "a powerful tool in persuading practitioners and laymen alike of the authority of the mason's craft," says Hislop.
This article was originally published by WIRED UK
