A Geometric Solution of a Cubic by Omar Khayyam ... in Which Colored Diagrams Are Used Instead of Letters for the Greater Ease of Learners

The visual language employed by Oliver Byrne in his 1847 edition of Euclid's Elements provides a natural syntax for communicating the geometrical spirit of Omar Khayyam's 11th-century constructions for solving cubic equations. Inspired by the subtitle (co-opted for this article) from Byrne's The Elements of Euclid, we rework one of these constructions by adapting his distinct pictographic style. This graphical presentation removes the modern reliance on algebraic notation and focuses instead on a visualization that emphasizes Khayyam's use of ratios, conic sections, and dimensional reasoning.