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. There is a cubic polynomial which has a single variable, \(x\), and its highest exponent is 3: [f(x): a x^3 + b x^2 + c x + d = 0,] ...
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...
