If the range of Bless is 30ft and the Cleric is 30ft in the air, then any non-zero horizontal distance would technically put them out of range. You don't need to calculate that they are 36.06ft away to know if they are out of range or not.

But do their feet need to be in range or just a single part of their body?

Depends on which part of them needs to be blessed?

But D&D uses Chebyshev distance, not Euclidean. No need for Pythagoras. And Pathfinder alternates between Chebyshev and Manhattan to *approximate* Euclidean.

Do some people actually playing RPG care that much about range ? Rather than some guesstimate ? I actually find the Ryuytama range management pretty cool, where you simply say whether your character is *at contact/short-range/long-range/away* and that's it.

Some do. I like positioning on a grid as a part of combat. It rewards tight play and understanding the mechanics. When I DM though, it depends on the playgroup. I think most people prefer guesstimating and just applying the rule of cool

Me at 20: I'm never going to need Chebyshev distance in real life. Why am I learning this?

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.

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.

IMHO, one of the more intriguing effects of streaming live-play series thriving these days has been the rise of TotM elements, if not entire games. Whereas my on-ramp to the hobby, et al, was finding a garage sale copy of the red box, the new crowd is cutting their teeth as spectators — and avid, creative spectators that most often are inspired to then recapture that feeling in-person or live online with others. I love that imagination is winning out over consumerism, at least in this small corner.

Depends how tall they are.

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^∞^).

Playing combat on a grid is actually presented as an optional rule and not the default for 5E, despite its popularity

So are feats, and point buy.

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.

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.

There's no grid in the sky, though

Holy shit it does. The halfling and dwarf are out of luck. Human stands a chance.

If you actually have to use that much math more than once in a blue moon, you're doing it wrong.