Geometric Properties of Planar and Spherical Interception Curves
  • View Times: 25
  • |
  • Release Date: 2023-08-07
  • plane curve
  • spherical curve
  • non-linear ODE
  • pursuit curve
  • Mercator projection
  • Gudermannian function
  • lemniscate constants
  • Gauss’s constant
  • spherical spiral
  • loxodrom
  • rhumb line
  • stereographic projection
  • logarithmic spiral
Video Introduction

This video is adapted from 10.3390/axioms12070704

The study of curves and their geometric properties is one of the oldest topics in mathematics. There are many interesting curves on a plane or sphere that are defined kinematically or geometrically and can be studied using the methods of calculus, differential equations, and differential geometry. For example, on a plane, one can mention tractrix, pursuit curve, lemniscate, brachistochrone, cycloid, conchoid of Nicomedes, limaçon of Pascal, etc., and on sphere great circle, spherical spiral, which is a special case of loxodrome also known as rhumb line, etc.

Full Transcript
Video Production Service