Homotopy for the constant path and the circle.[br][br]Let [math]g: [0,1]\rightarrow R^2- \{0\}[/math] defined by [math]g(s)=(\cos(2\pi s), \sin(2\pi s))[/math] and [math]g'(s)=(1,0)[/math] for all [math]s\in [0,1][/math].[br][br]The homotopy is defined by [math]H(s,t)=(\cos(2\pi s (1-t)), \sin(2\pi s (1-t)))[/math] for [math]s,t \in [0,1][/math].