Tag: Algebraic

I tried my best to guide a fine-tuned GPT model (using GPT-4 as my baseline model) to help hone in on the meanings of these properties in ways that a 2nd grader could grasp. What I got was interesting, to say the least. 1. Reflexive Property of Equality means that anything is equal to itself. Thi...

Since our middle school or high school years, we have learned that by using only a compass, which can only transfer a known length, and a straight edge, which can only draw a straight line, one can not trisect a given angle. This old truth was found in the early years of Greek geometry, but it is on...

Algebraic geometry is a captivating branch of mathematics that studies solutions to polynomial equations. One of the fundamental objects of study in this field is algebraic curves, which are defined by polynomial equations in two variables. Among these curves, the quartic curve holds a special place...