Abstract
Any L p -metric (as well as any norm metric for a given norm | | . | | on \(\mathbb{R}^{2}\)) can be used on the plane \(\mathbb{R}^{2}\), and the most natural is the L 2-metric, i.e., the Euclidean metric \(d_{E}(x,y) = \sqrt{(x_{1 } - y_{1 } )^{2 } + (x_{2 } - y_{2 } )^{2}}\) which gives the length of the straight line segment [x, y], and is the intrinsic metric of the plane.
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Deza, M.M., Deza, E. (2016). Distances on Real and Digital Planes. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52844-0_19
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