# Geometry/Differential Geometry/Introduction

One goal of differential geometry is to classify and represent differentiable curves in ways which are independent of their paramaterization. For example consider the curve represented by ${\displaystyle y=3x}$. Although ${\displaystyle (x,y)=(t,3t)}$ and ${\displaystyle (x,y)=(3t,9t)}$ are different paramterizations, they both represent the same curve. More generally, we consider the slope of the curve ${\displaystyle 3={\frac {dy}{dx}}={\frac {dy}{dt}}\cdot {\frac {1}{\frac {dx}{dt}}}={\frac {3}{1}}}$.