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Math Matters
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But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to *approximate* Euclidean.i wish that it was more common to refer to the metrics in terms of what they are instead of who discovered them. i can’t ever remember off the top of my head if the chebyshev one is supposed to be the diamond metric (L^1^) or the square metric (L^∞^).
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But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to *approximate* Euclidean.
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Playing combat on a grid is actually presented as an optional rule and not the default for 5E, despite its popularitySo are feats, and point buy.
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i wish that it was more common to refer to the metrics in terms of what they are instead of who discovered them. i can’t ever remember off the top of my head if the chebyshev one is supposed to be the diamond metric (L^1^) or the square metric (L^∞^).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.
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That is one reason I don't like D&D, it is a glorified boardgame the hides it's wargame roots under a very thin layer. I like tactical rpg on the computer but investing that level of math and detail in a pen & paper game is so boring, for me at least.My group plays pretty loose goosy with the rules. We just look at it and make a quick estimate of whether something looks in range. They also have little range finder tools that are helpful for quickly determine cones, spheres, etc. We're also the kind of party that doesn't really keep track of gold. Apparently gold has a weight? For this reason I actually don't like playing one shots with people I don't know, because they don't play by all of our house rules, lol.
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But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to *approximate* Euclidean.There's no grid in the sky, though
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That is one reason I don't like D&D, it is a glorified boardgame the hides it's wargame roots under a very thin layer. I like tactical rpg on the computer but investing that level of math and detail in a pen & paper game is so boring, for me at least.If you actually have to use that much math more than once in a blue moon, you're doing it wrong.
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There's no grid in the sky, thoughFair point. I actually don't know what, if anything, the D&D (or Pathfinder) rules say on this matter. I've always just treated it as a natural 3D extension of the 2D grid rules. If they're three squares in one direction, same square in the other, and 10 feet up, I'd treat that as 15 feet away because of Chebyshev rules.
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The opposite of that happened to Achilles
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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 distance 1. i’ve found this wikipedia picture to be very helpful, and the diamond/square/circle terminology is my way of paying my respect to the picture. 
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If you actually have to use that much math more than once in a blue moon, you're doing it wrong.
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My group plays pretty loose goosy with the rules. We just look at it and make a quick estimate of whether something looks in range. They also have little range finder tools that are helpful for quickly determine cones, spheres, etc. We're also the kind of party that doesn't really keep track of gold. Apparently gold has a weight? For this reason I actually don't like playing one shots with people I don't know, because they don't play by all of our house rules, lol.In general I don't really like Pen&Paper RPGs where you need miniatures (and for worse range finder tools) to play them. But that is a me thing, don't read my words as that I want to say D&D should change. Far away from that, D&D is a great game and I love it on the PC (where it IMHO only works, not at the table)
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Me at 20: I'm never going to need Chebyshev distance in real life. Why am I learning this?Happy cake day!
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Happy cake day!Happy cake day to you!
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But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to *approximate* Euclidean.Is that so? Why would some spells specify geometry then? For example fireball says it is a 20 ft *radius* while Hallucinatory Terrain specifies that it affects a 150 ft *cube* which, under Chebyshev distance, would be the same as a sphere right? My understanding was that D&D 5e uses euclidean distance with a minimum threshold of a square that has to be covered to be counted.
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Is that so? Why would some spells specify geometry then? For example fireball says it is a 20 ft *radius* while Hallucinatory Terrain specifies that it affects a 150 ft *cube* which, under Chebyshev distance, would be the same as a sphere right? My understanding was that D&D 5e uses euclidean distance with a minimum threshold of a square that has to be covered to be counted.
