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Math Matters (lemmy.world)

submitted 4 months ago by Stamets@lemmy.world to c/rpgmemes@ttrpg.network

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[–] affiliate@lemmy.world 10 points 4 months ago* (last edited 4 months ago) (1 children)

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.

[–] Zagorath@aussie.zone 7 points 4 months ago (1 children)

Ah right, so "diamond" (depicted as a square rotated 45 degrees) is Manhattan, circle is Euclidean, and square is Chebyshev, then?

[–] affiliate@lemmy.world 5 points 4 months ago

yeah exactly. i understand it as follows:

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 x^2^ + y^2^ = 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.