Collapsing then Expanding the Equation for a Sphere
[caption id="attachment_8626" align="alignright" width="480"] How simple is a sphere?[/caption] Equation for the Simplest Sphere The equation for a sphere with its center at the origin is: x2 + y2 + z2 = c2 Where c is a positive constant. For simplicity, let's choose a positive constant, k, such that k = c2. Equation for a Circle by Collapsing a Sphere Collapsing it in one dimension generates the equation of one of three circles: x2 + y2 = k x2 + z2 = k y2 + z2 = k Equation for a Point by Collapsing a Circle Collapsing the three circles in one dimension generates two equations representing precisely two points for each of them: For x2 + y2 = k, x²2 = k y2 = k For x2 + z2…