Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Two Points Plus One Line
Stage: 4 Challenge Level:
This problem gives an opportunity to find the parameters that
express the generality in the context.
For example, if the distance between the feet of perpendiculars
dropped from $A$ and $B$ is taken as the unit length, then the
length of the perpendiculars can be expressed in terms of that
There may be other useful unit lengths to consider, but the
important skill is to see that enlarging the diagram doesn't change
the feature being explored, so a thoughtful choice of unit can help
to make the problem more convenient to handle and access.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.