Construction Design Mathematics: the Angel Choir Window in Lincoln Cathedral

The Angel Choir window in Lincoln Cathedral

Once a single or pair of lights surmounted by a quatrefoil within a circle had been constructed (see relevant lesson plans), masons were quick to realise its potential for larger areas, by increasing the number of lights and circles. Large C13th windows of the Geometric period had an even number of lights arranged in pairs, each pair with its own circle. The largest example is the eight-light Angel Choir window in Lincoln Cathedral where the window is made up of eight lights, arranged singly, yet in pairs, and also in fours, i.e. two times two pairs, or four + four lights, with a total of thirteen circles of different sizes in the window apex.

School Curriculum: Key Stage 4 Mathematics:

The Sine Rule.

In a similar way to the apex window at Altrincham Baptist Church, and the mouchette wheel at St Thomas of Canterbury, Northaw, (see relevant lesson plans) the circular window in the apex of the Angel Choir window at Lincoln Cathedral required builders to find appropriate centres of the inscribed congruent, circular windows, or circles.

In the Angel Choir window, there are six circles, each tangental to the circumscribing circle, and to two neighbouring inscribed circles. There is also one inner circle; with the inner circle being inscribed by the six inscribed outer circles.

Applying the sine rule provides a formula for finding the radius (rs) of any number of inscribed circles where (rl) = radius of the circumscribing circle, and angle x are known.

Photo credit: Jules & Jenny