Construction Design Mathematics: the development of a horseshoe arch

In Asia Minor the horseshoe arch has long been a structural and decorative motif adorning tombs, sarcophagi and stele. After the Eastern Christian Church adopted the shape it quickly spread to North Africa, Spain, Gaul, Italy and Rome itself.

How to draw a horseshoe arch:

School curriculum: Key Stage 4: measurement of arc length

Maths covered:
Arc length is the distance between two points on a curve. and is usually denoted by l or s, the latter from the Latin spatium meaning length or size.
s = (θ° ÷ 360°) x 2 π r

where theta θ is a measure of the angle subtended by either ci-e-di & co-e-do (fig. on lesson plan in degrees, π = 3.14 and r = the distance ae (fig.) in centimetres

If the arc is a semicircle
then s = π r

This lesson would serve as an extension of the lesson on a Roman arch and brace, itself extended by the lesson on a Romanesque or Norman arch