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

{| width = "100%"

|- ! colspan="3" align="center" | Mathematics desk |- ! width="20%" align="left" | < November 8 ! width="25%" align="center"|<< Oct | November | Dec >> ! width="20%" align="right" |Current desk > |}

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

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

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

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

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