My Discovery of New Equations in the Conic Sections: (My Stuff Is Understandable…Fermat’s Last Theorem Is Not)

This is a conversational tone piece that’s not meant to be mathematical. In fact no math at all will be present. I just want to discuss how creative my endeavor was that I wrote extensively about in my math book.

Points, Lines, and Conic Sections: A Sequel to College Algebra

My discoveries lie in the area of mathematics called the conic sections. This is very low level stuff. It’s hardly the place where one would even think to look for new formulas since they have been teaching this material for a couple of centuries now. Fermat’s Last Theorem, for example was a known unsolved problem for over three centuries until Andrew Wiles solved it, but very few people can understand the proof because it is so deep.

The 1670 edition of Diophantus’s Arithmetica includes Fermat’s commentary, referred to as his “Last Theorem” (Observatio Domini Petri de Fermat), posthumously published by his son.

So, think of all these teachers teaching about lines and slopes. Then, in a chapter or two, they teach about parabolas. Along the way, they cover things like the slope formula and the distance formula.

It’s all right there. Why didn’t anybody ever ask, “Hey, what if you put a line through a vertex (or focus)…