Personally I find Euclidean easy to remember because it matches the much more general Euclidean geometry. So you just remember “this is like, real maths”. Manhattan distance is easy to remember because it does basically “refer to the metrics in terms of what they are”, so long as you remember that Manhattan famously is a grid. Chebyshev is the hardest, but for me it’s a simple matter of “the one that’s left over”.
I have no idea, based on the name, what diamond and square metrics are supposed to be.
i think that’s a good point and that is a nice way to remember them. i think a lot of it just comes down to personal preference.
i like calling them the diamond/square/circle metrics because those shapes describe the sets of points that have unit length. i’ve found this wikipedia picture to be very helpful, and the diamond/square/circle terminology is my way of paying my respects to the picture.
in the manhattan metric, points have length one if the lengths of their coordinates sum to 1. so you get the points (1, 0), (0, 1), (-1, 0), and (-1, -1). and then you connect these four points with straight lines to get the diamond shape. this follows from the observation that if the x coordinate decreases in length by 0.1, then the y coordinate must increase in length by 0.1.
in the euclidean metric, the points of length one lie on the unit circle, since x2 + y2 = 1 is the equation defining the unit circle.
in the chebyshev metric, points have length 1 if one of the coordinates has length 1 and the other coordinates have a length smaller (or equal to) 1. and these conditions also describe the square with sides x = ± 1 and y = ± 1.
Personally I find Euclidean easy to remember because it matches the much more general Euclidean geometry. So you just remember “this is like, real maths”. Manhattan distance is easy to remember because it does basically “refer to the metrics in terms of what they are”, so long as you remember that Manhattan famously is a grid. Chebyshev is the hardest, but for me it’s a simple matter of “the one that’s left over”.
I have no idea, based on the name, what diamond and square metrics are supposed to be.
i think that’s a good point and that is a nice way to remember them. i think a lot of it just comes down to personal preference.
i like calling them the diamond/square/circle metrics because those shapes describe the sets of points that have unit length. i’ve found this wikipedia picture to be very helpful, and the diamond/square/circle terminology is my way of paying my respects to the picture.
Ah right, so “diamond” (depicted as a square rotated 45 degrees) is Manhattan, circle is Euclidean, and square is Chebyshev, then?
yeah exactly. i understand it as follows: