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Using familiar properties of norm and inner product, we will prove a new inequality concerning distances between each pair of n points in an inner product space, where n is an integer larger than 3 . Moreover, we investigate the Aleksandrov-Rassias problem by proving that if the distance 1 is contractive and the golden ratio is extensive by a mapping f , then f is a linear isometry up to translation. Mathematics subject classification (2010): 51M16, 51K99, 51K05, 46C99.

An inequality for distances among five points and distance preserving mappings