What Every Programmer Needs To Know About Conic Sections (To Attack Bitcoin)

A Comprehensive Introduction to the Matrix Theory of Conic Sections

Circles, parabolas, ellipses and hyperbolas are generally called conic sections or conics, because they result from intersecting a cone with a plane as shown below (Stewart, 2016)¹ :

Intersecting a cone with a plane taken from (Stewart, 2016)

Conic sections were discovered by Menaechmus in 350 BC, and most of the theory was well known to the ancient Greeks down to the time of Pappus of Alexandria (Coolidge, 1945)². The study of conic sections is well over 2000 years old.

This articles serves as a programmer’s introduction to conics and the related matrix theory.

Our primary sources are:

1. Geometry by David Brannan, Matthew Esplen and Jeremy Gray. (Brannan et al., 2012)³

2. Treatise on Conic Sections by Appolonius of Perga and adapted by T.L Heath. (Heath, 1896)⁴