Construction Design Mathematics: a circle, elliptical & ogee curve or mouchette

School Curriculum: Key Stage 3 & 4 Mathematics: drawing angles using a pair of compasses and a straight edge; centroid of a triangle; congruent circles within a circle: manipulating shapes, Pythagoras Theorem and the sine rule; Properties of 30°-60° 90° triangle:

Drawing a mouchette is based on circle stacking, i.e. arranging three congruent circles within a circle. The window at St Thomas of Canterbury, Northaw required builders to find appropriate centres of the smaller congruent cirlces when the larger circle had been designated. To effect this the design could often be manipulated mathematically to produce a triangle that in turn enabled calculation of sides or angles by the 30° -60° -90° rule if a right angle was present.

It was a short step from the reticulated Curvilinear tracery (see relevant lesson plan) to the use of a mouchette as a motif. A mouchette is a daggerlike motif found most often in 14th century Decorated church tracery. It is formed by elliptical and ogee curves that produce a point at one end and an incomplete circle at the other.