Construction Design Mathematics: a Gothic vesica & a triquetra

How to draw a vesica piscis

School curriculum: Key stage 3 mathematics

Mathematically this shape is termed an ellipse and is produced when two circles of the same radius intersect such that the centre point of each circle lies on the circumference of the other, with both circular elements being smaller than a semicircle. The two circular elements would also join along their chords. It extends the introductory exercise constructing a perpendicular bisector.

The shape should recall the first steps in the construction of an isosceles or equilateral triangle (see separate lesson on drawing a lancet arch). The equilateral triangle has as its verteces the centre points of the two circles and one of the two sharp corners of the vesica piscis

The area of an ellipse is also twice that of a the pointed arch section of a lancet window.

Drawing a triquetra (a pointed trefoil) extends the subject.

School Curriculum: Key Stage 2 & 3 mathematics: A pointed trefoil may be turned about its centre point into three identical positions, i.e. it has rotational symmetry of order three.

A triquetra, from the Latin for three corners. comprises three circular arcs of equal radius. The exercise extends the work on a purpendicular bisector and a vesica piscis.