Cathedral Windows and Stone Circles
Medieval Stonemasons were adept practical geometers, using compasses, set-squares and plumblines. For example, they designed curving windows using just arcs of circles, such as those
illustrated below.
Lancet Arch:
Draw a line and construct a perpendicular on this line.
Make points that split the original line into quarters.
These form the centre points for your arcs.
Ogee Arch:
Construct a line and it’s perpendicular
bisector.
Construct a circle using the intersection of
these two lines as a mid point (A) the original
line as the diameter.
Construct two 60º angles at A.
Hence mark points B and C.
Find points D and E, so that AB=AC=CD=BE
Points D and E are the centres of the
remaining two arcs.
Basket Arch (Three centred arch)
Draw a line AB.
Construct the equilateral triangle ABC.
Mark the midpoint of AB, D and use this
to construct two circles centred at A and
B.
Extend the line CA to meet the circle at
E.
Extend the line CB to meet the circle at
F.
Construct the large circle centred at C
Four centred arch:
Construct a square ABCD. Find the midpoint of AD; label this E and
construct the four small circles centred on A, B, C and D.
Draw in the lines through AC and BD. Mark the intersections F and G.
Draw the two large circles centred at A and D.
Many of the ancient stone circles found in Britain are in fact not completely circular. They are
formed from circular arcs as follows:
Construct a square ABCD. Mark a point E at your choosen distance on the projection of AB.
Construct a circle centred at A, radius AE.
Mark point F at the intersection of this circle and the projection of AD.
Construct a circle centred at D, radius DF.
Construct a circle centred at B, radius BE.
Mark point G at the intersection of this circle and the projection of CB.
Construct the circle centred at C, radius CG.
Inspired by OU resource for ME825.
Created by KSH Sept 2007