Math Matters
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Depends on which part of them needs to be blessed?
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 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.
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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.
If I think more about it i come to conclusion that is not really the math per se, but what I find boring is that 90% of the rules (measured by feeling) are about battle and battle takes such a huge and detailed part in the game.
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If the cleric is 30ft in the air, and the allies are 20ft away but on the ground, then the allies are probably 10ft tall
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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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And multiclassing.
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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.
Fireball says radius, but in a non-Euclidian geometry radius doesn’t translate to a Euclidian sphere. Embrace the cube of constant radius!
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Fireball says radius, but in a non-Euclidian geometry radius doesn’t translate to a Euclidian sphere. Embrace the cube of constant radius!
Right, but again why would it draw a distinction between “20 ft radius sphere” and a “cube” in different spells? Would they not all be “spheres” is that is truly how the game is meant to be played?
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Fair 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.
In PF1e you’d still alternate between Manhattan and Chebyshev. I used to know the rules to that so well I’d run it without the book for reference.
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Right, but again why would it draw a distinction between “20 ft radius sphere” and a “cube” in different spells? Would they not all be “spheres” is that is truly how the game is meant to be played?
Have you actually read the rules? The game, as written, isn’t really meant to be played at all. It just vaguely gestures at activities and suggestions, and if you look too closely you’ll find a lot of junk that doesn’t fit or doesn’t really work.
People don’t play 5e. People leverage 5e’s one core feature and then build their own games around it, ignoring most of the published rules.
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Have you actually read the rules? The game, as written, isn’t really meant to be played at all. It just vaguely gestures at activities and suggestions, and if you look too closely you’ll find a lot of junk that doesn’t fit or doesn’t really work.
People don’t play 5e. People leverage 5e’s one core feature and then build their own games around it, ignoring most of the published rules.
I don’t fully disagree with you, but you’re just wrong about the area of effect shapes. The rules are very defined on how to represent and find spheres, cylinders, lines, cubes, cones, etc. The new 5.5 rules make it even more defined. The game is absolutely designed to be played as written, because it’s braindead easy compared to most systems, which is basically all 5e has going for it: easy to learn and run, easy to homebrew. Every DnD 5e game I’ve played has followed the rules, not just for areas, but most mechanics, especially when using actual battle maps. Theater of the mind gets a bit more loosely goosey. Every group has their own house rules, but the game is definitely meant to be played, and it is. It almost seems weird to even make that claim, because a quick trip to a LGS or playing in a few local groups would tell you otherwise. Everyone wants to be Critical Role or Dimension 20.
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I don’t fully disagree with you, but you’re just wrong about the area of effect shapes. The rules are very defined on how to represent and find spheres, cylinders, lines, cubes, cones, etc. The new 5.5 rules make it even more defined. The game is absolutely designed to be played as written, because it’s braindead easy compared to most systems, which is basically all 5e has going for it: easy to learn and run, easy to homebrew. Every DnD 5e game I’ve played has followed the rules, not just for areas, but most mechanics, especially when using actual battle maps. Theater of the mind gets a bit more loosely goosey. Every group has their own house rules, but the game is definitely meant to be played, and it is. It almost seems weird to even make that claim, because a quick trip to a LGS or playing in a few local groups would tell you otherwise. Everyone wants to be Critical Role or Dimension 20.
erin (she/her) said in Math Matters:
I don’t fully disagree with you, but you’re just wrong about the area of effect shapes. The rules are very defined on how to represent and find spheres, cylinders, lines, cubes, cones, etc.
You understand that I was making a joke, right? “Embrace the cube of constant radius!”?
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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.
D&D’s targeting rules are quite strange, but yes, it’s very explicit that Chebyshev is used in 5e by default, if playing on a grid. On page 192 of the 5.0e PHB:
To enter a square, you must have at least 1 square of movement left, even if the square is diagonally adjacent to the square you’re in.
The DMG presents, on page 252, an optional variant of the optional grid rules, which is to treat it the same as Pathfinder 2e does (alternating 5 ft and 10 ft):
The Player’s Handbook presents a simple method for counting movement and measuring range on a grid: count every square as 5 feet, even if you’re moving diagonally. … This optional rule provides more realism.
When measuring range or moving diagonally on a grid, the first diagonal square counts as 5 feet, but the second one counts as 10 feet. This pattern…continues when you’re counting diagonally even if you move horizontally or vertically between different bits of diagonal movement.
As for the value of cube vs sphere in the context of Chebyshev ranges, there are two key differences.
First, cubes measure side length, spheres measure radius. A 10 ft cube covers 4 squares. A 10 ft sphere covers 16.
Second, and more importantly (since the above could easily be translated by using only cubes or only spheres throughout the system, with either half or double the numbers), cubes are cast from one side, whereas spheres are cast from the centre. If you’re standing in the front line with enemies in front of you and allies behind, a cube cast with you as its origin point will hit either allies only or enemies only, but not both. A sphere cast with you at its origin point will affect both allies and enemies. Note that the rules for cube, on page 204 of the 5.0 PHB say “A cube’s point of origin is not included in the cube’s area of effect, unless you decide otherwise.” So you could include yourself and your allies, or you could include enemies but not yourself, if you so desired. Or, less likely, you could include allies but not yourself, or enemies and yourself.
From memory, cube spells are mostly cast from a range of “self”, which is where this becomes an important distinction. If a spell has a range of X feet and cube, then the main difference is just that its area is smaller but its reach is longer than a sphere with the same numbers.
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In PF1e you’d still alternate between Manhattan and Chebyshev. I used to know the rules to that so well I’d run it without the book for reference.
As it happens I’ve just looked up the 5e rules for this for the sake of another comment, and their rules are that, like PF1e, if you go vertical, you follow the same rules (i.e., Chebyshev by default, optional alternating) as on a flat plain.
I’ve not looked up the PF2e rules, but I feel safe in assuming it’s the same in this regard as 1e.
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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?
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Except the game uses Chebyshev distance, so as long as they’re within 30 feet in the x, y, and z dimensions, they’re within 30 feet.
Though for area damage spells, it’s much, much more complicated. You don’t just have to find the Euclidean distance from them to the center. You have to calculate how much of their square is within that distance.
Though for area damage spells, it’s much, much more complicated.
That’s an optional variant rule described in Xanathar’s Guide. The default rule for grids is simpler: just do Chebyshev.
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erin (she/her) said in Math Matters:
I don’t fully disagree with you, but you’re just wrong about the area of effect shapes. The rules are very defined on how to represent and find spheres, cylinders, lines, cubes, cones, etc.
You understand that I was making a joke, right? “Embrace the cube of constant radius!”?
I’m more concerned with the “people don’t play the rules” part, but fair enough.
