This is a solution to the problem "A Quick Puzzle — Find x" posted 1/9/26.
Comment Trisecting an angle with straightedge and compasses was a problem posed in antiquity and which many mathematicians attempted to solve over the ages, until Wantzel proved it was impossible in 1837.
So have we achieved the impossible? Well, no. The original problem assumed the use of an unmarked straight edge, and our construction requires one we can mark. Or we could use three rods of equal length.
Our construction formed the basis of an angle trisection method given by Étienne Pascal, father of Blaise, he of the triangle which you will recognise
1 1
1 2 1
1 3 3 1
1 4 6 4 1
However what was essentially the same method was already known to Archimedes over a millennium earlier.
There is an old joke allegedly from a real exam script
