The content in this section is not a traditional set of well-polished and elegant solutions to given problems but rather my attempt to record, as truthfully as possible, the process of an actual search for a solution with all of its false starts, dead ends, stutters and failures.
On a technical note we remark that in this section and elsewhere we shall refer to the theorems from Euclid's "Elements" in the form of BnPm where n designates the book and m designates the proposition number. For example, B3P32 stands for Book 3 Proposition 32 and so on.
We define a geometric construction step as an act of drawing a new, previously not existing, line - either a straight line or a circle. Extending a given line segment, ray or a circular arc in either direction does not count as a step. Picking an arbitrary point or naming an intersection of two or more objects also does not count as a step.
In the never ending optimization quest popular in mathematics and computer science we seek a solution to a given problem that takes the least amount of steps.
\(\blacksquare\)