Abstract:Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus $\mu _{_X}$ of the normed space $X$. The values of the rectangular modulus at some noteworthy points are well-known constants of $X$. Characterizations (involving $\mu _{_X})$ of inner product spaces of dimension $\geq 2$, respectively $\geq 3$, are given and the behaviour of $\mu _{_X}$ is studied.
Keywords: characterizations of inner product spaces, orthogonality, moduli of Banach spaces
AMS Subject Classification: 46C15, 46B20