In performing an exercise of “What if not”, one can end up with a paucity of structure. Adding alternative structure can be a rich source of discovery, as we present here. The framework of this presentation is the original voyage of discovery, from a trivial geometric problem to the derivation of some unexpected trigonometric formulae based on regular polygons. The original “voyage” has been changed only sufficiently to make the text readable.
"If not, then what if as well- Unexpected Trigonometric Insights,"
The Mathematics Enthusiast: Vol. 9
, Article 2.
Available at: http://scholarworks.umt.edu/tme/vol9/iss1/2