I am struggling to understand how the curvature of a hypersphere decreases as its radius increases? The Wikipedia article on hypersphere does not give a mathematical or intuitive reason as to why this happens.
If anyone could explain how changing radius effects the hypersphere. The volume of the hypersphere is given by $\frac{\pi^2r^4}{2}$ where $r$ is the radius of the hypersphere. I want to know how hypersphere changes if $Lim_{r\rightarrow\infty}(\frac{\pi^2r^4}{2})$.
Thanks.