Construction Design Mathematics: Gothic architecture: a lancet window

Introduction to Gothic architecture

How to draw a pointed arch or a pointed (lancet) window

School curriculum: Key Stage 2 mathematics: Equilateral and isosceles triangles. Draw attention to the lancet arch being set out on the vertices of an equilateral triangle .
Placing the compass point on wider or narrower loci on the horizontal plane will produce broader or narrower arches respectively. In these cases the lancet arch is set out on the vertices of an isosceles triangle.

KS4 Mathematics: The drawing can be a suitable adjunct to a lesson on constructing an equilateral triangle or isosceles on a given straight line, or where the altitude or height of the triangle is given. For proof of centroid of triangle see appropriate lesson plan.

The drawing can also support teaching the formula for measuring arc length, usually denoted by s.
s = θ° ÷ 360° x 2 π r

or sector area, where A = θ° ÷ 360° x π r²

An elegant window is usually achieved when the height of the window is eight times the width.

Further lessons developing the study of a lancet arch can be seen on lesson plan Gothic architecture: lancet triplets, and Gothic architecture: window with intersecting or Y-shaped tracery.