PROOF of a (Mathematical) Geometrical discovery of 1961- HOW TO CONSTRUCT A PYRAMID REQUIRING A GIVEN HEIGHT with a given base-length USING ONLY RULER, COMPASS, AND PENCIL.

In Mechanical Drawing class, 1960 or 1961, we were to construct some basic platonic solids with compass and ruler. The problem was to construct a square pyramid with base length of 2a and height of b. W is the center of the square base. (I give these variables, as I cannot remember the actual numbers.) Our textbook stated that this could only be done by trial and error—there was no way to construct this pyramid with just a ruler and compass. The method of trial and error the book showed was very tedious. I was too lazy for trial and error-- I had to find another way.