Altitude properties and characterizations of inner product spaces |
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Authors: | Edward Andalafte Raymond Freese |
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Institution: | 1. Department of Mathematics, University of Missouri - St. Louis, 63121, St. Louis, MO, USA 2. Department of Mathematics, Saint Louis University, 63103, St. Louis, MO, USA
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Abstract: | New characterizations of real inner product spaces (euclidean spaces) among metric spaces are obtained from familiar formulas expressing the altitude (height) of a triangle as a function of the lengths of its sides. Other properties related to the altitude of a triangle are also shown to result in characterizations of euclidean spaces, or euclidean and hyperbolic spaces. |
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