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Keywords:
chordal orthogonality; Feuerbach circle; inner product space; James orthogonality; Minkowski plane; normed linear space; normed plane; orthocentricity; Wallace line
chordal orthogonality; Feuerbach circle; inner product space; James orthogonality; Minkowski plane; normed linear space; normed plane; orthocentricity; Wallace line
Summary:
In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions $d\geq 3$.
References:
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