Monday, November 30, 2009

Mathematics and Gothic Cathedrals





Strait from scratch, Gothic architects constructed ground plans and calculated elevation using basic geometric forms like polygons, particularly the square. These methods of building were kept a secret until the end of the cathedral age when they were finally released by a man by the name of Matthäus Roriczer. In the figure in the left-above Roriczer teaches people how to create elevation from a ground plan by mean of a single square. The demensions are related to one another like the sides of a sequence of squares so that the area decreses or increases in a geometrical progression.

Another famous Gothic architect was Villard de Honnecourt. In the figure right-above De Honnecourt shows how to the true proportions for the ground plan of a cloister by halving the square. At the center of the cloister is the cathedral steeple. Like Roriczer's plan, the steeple uses area of the squares decrease in a geometrical progression all the way to the top.

Toward the end and slow down of the cathedral age, architects in Milan started determining geometric formulas that used the equilateral triangle to form more intricate and detailed cathedrals. However, the square remained the favorite and is still the basis for all Gothic architecture today.