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On area and side lengths of triangles in normed planes

Gennadiy Averkov, Horst Martini (2009)

Colloquium Mathematicae

Let d be a d-dimensional normed space with norm ||·|| and let B be the unit ball in d . Let us fix a Lebesgue measure V B in d with V B ( B ) = 1 . This measure will play the role of the volume in d . We consider an arbitrary simplex T in d with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of V B ( T ) are determined. For d ≥ 3 it is noticed that the tight lower bound of V B ( T ) is zero.

On Gnomons

Jan M. Aarts, Robbert. J. Fokkink (2003)

Matematički Vesnik

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