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Jarnik's identity plays a major role in classical simultaneous approximationto two real numbers. O. German [2] has shown a generalization to the weightedsetting in which the identity has to be replaced by two inequalities. Hismethods belong to classical geometry of numbers. The aim of this paper is toprovide an alternative approach based on a careful examination of certainsuccessive minima functions that stem from parametric geometry of numbers, amethod that has already been successfully employed to generalize Jarnik'sidentity to higher dimensions in the classical setup in [3] and [7].

A geometric proof of Jarnik's identity in the setting of weighted simultaneous approximation