Wikipedia:Reference desk/Archives/Mathematics/2022 November 9

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November 9

between chessboard distance and taxicab distance in higher dimensions

Looking at Chebyshev distance, which also links to Manhattan distance, I thought about intermediates. In three dimensions there is what I privately call the garnet distance: max(|∆x|+|∆y|,|∆x+∆z|,|∆y+∆z|) – it defines a ball in the shape of a garnet crystal, a rhombic dodecahedron. Generalizing to n dimensions, the k-garnet distance is the maximum of the sum of any k coordinate distances, 1≤k≤n (1: Chebyshev; n: Manhattan).

Has anyone made use of such intermediate measures? —Tamfang (talk) 18:01, 9 November 2022 (UTC)

I think you meant to write

$\max(|\Delta x|+|\Delta y|,|\Delta x|+|\Delta z|,|\Delta y|+|\Delta z|).$

 --Lambiam 20:02, 9 November 2022 (UTC)

Er, yes. —Tamfang (talk) 08:46, 10 November 2022 (UTC)