Construction Design Mathematics: Gothic Geometric tracery: a trefoil within a circle

How to draw a trefoil within a circle

School Curriculum: Key Stage 4 mathematics: The trefoil within a circle extends the work on trefoils. In a trefoil a circle circumscribes the three vertices of a triangle. This enables the placement of the three foils or arcs centred on each of the verteces of the triangle. Here the exercise is repeated but with the addition of a circumcircle, still centred on the circumcentre, i.e. the centre of the triangle, but at a tangent to each of the three foils. Extra decorative arcs embellish the work.

The trefoil was brought to England by French masons in the first half of the thirteenth century. Binham Priory in Norfolk, now a romantic ruin, then a thriving Beneditine monastery, vies with Westminster Abbey as the location in which it first appeared.