This article explains how to solve roots of a quartic polynomial in the complex plane. I use the depressed form of the quartic polynomial and Descartes’ method. Additionally, I demonstrate an interactive demo which visualizes the roots of a quartic polynomial.
This article explains how to solve roots of a cubic polynomial in the complex plane. I use the depressed form of the cubic polynomial and Cardano’s formula. Additionally, I demonstrate an interactive demo which visualizes the roots of a cubic polynomial.
Projecting a 3D object onto a 2D plane often involves transforming geometric equations into a perspective view. Here’s a fun observation: when you view a parabolic curve drawn on the xz-plane from the xy-plane through a perspective projection, the curve can appear as an ellipse. The animation ...
This post explains the mathematical principles and dynamics of elliptical orbits in celestial mechanics. To fully grasp how planets move and where they are at any given time, it begins by introducing the concept of planetary orbits as ellipses, following Johannes Kepler’s first law of planetar...
