Mathematics

When Looking at a Parabola in Perspective

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 ...

Elliptical Orbit Geometry and Mechanics

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...