Inscribed Polygons that Characterize Inner Product Spaces

Carlos Benítez, Pedro Martín, Diego Yáñez

Let $X$ be a real normed space with unit sphere S. We prove that $X$ is an inner product space if and only if there exists a real number $\rho =\sqrt{(1+\cos \frac{2k\pi }{2m+1})/2}$, $(k=…