Formulas are derived, by direct integration of the defining definite integrals, for the general geometric mean distance between (i) a point and a line segment; (ii) a point and a rectangular area; (iii) two parallel line segments; (iv) two orthogonal line segments; (v) a line segment and a parallel-sided rectangular area; (vi) two parallel-sided rectangular areas. Certain useful identities of the formula for the last-named case are presented.
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Thomas James Higgins (1943) studied this question.
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