Planar Curves out of Their Curvatures in R2

Abstract

This research aims to introduce some of the main ideas of differential geometry. The research deals with the main concepts needed to understand this work. In this research properties of curves in 2 R are studied. The research is built on using the curvature of a curve in 2 R to derive a parametric formula for the velocity and acceleration. Also the geometry of focal points has been discussed. Examples are built to support the aim of this research.