Construction Design Mathematics: the Norman or Romanesque arch

A rich and elaborate construction of a Norman or Romanesque window.

School Curriculum: Mathematics at Key Stage 3: Constructing a Romanesque arch develops the geometric drawing skills of students. The resulting drawings can be a resource for the calculation of the area of a semi-circle using pi (π), and the perimeter of the semi-circle when the base (d or 2r) is known.

The construction can also be an application of the trapezoidal rule to calculate approximate area . The exercises extend the work on π, circles, semicircles and arcs following the drawings of a Roman arch and brace & the horseshoe arch, available elsewhere.

Maths covered

circumference of a circle = πd where d = diameter of the circle, where π = 3.14
= 2πr where r = radius of the circle

perimeter of a semicircle = (πd ÷ 2) + d

area of a circle = πr² area of a semi circle = (πr²) + 2

Constructing a Romanesque arch can be a practical application of the calculation of the area of a semi-circle using pi (π), and the perimeter of the semi-circle when the base (d or 2r) is known.

This lesson would be a development or extension of the lessons on a Roman arch & brace and / or the horseshoe arch.