Multiple Viewpoints Math Example 2

Solution

1. 1
   Algebraic viewpoint: $x^2+y^2=4$ is a Diophantine-type equation (or polynomial equation). Point: $(2,0)$ since $4+0=4$.
2. 2
   Geometric viewpoint: a circle of radius 2 centred at the origin. Point: any point at distance 2 from origin, e.g., $(\sqrt{2},\sqrt{2})$.
3. 3
   Parametric viewpoint: $x=2\cos t$, $y=2\sin t$, $t\in[0,2\pi)$. At $t=\pi/4$: $(\sqrt{2},\sqrt{2})$.