# D&D 4ENon-Euclidean Geometry in 4E?

#### Sir Sebastian Hardin

##### First Post
Stalker0 said:
I have to agree with teh mob here, I like the concept of 1 square in any direction.

ESPECIALLY with spell areas!! Figuring out a circle is hard harder on a hex graph than a square. Now I can just count out any side and go from there, I think its a lot easier.

Now the area of effect of my 20ft radius Fireball will be SQUARE!!!!!!!!!!!!!!! That's nonsense

I prefer any of the 3.x methods (Eventhough I like almost everything from 4th, btw)

Last edited:

#### TwinBahamut

##### First Post
The next size is 12 hexes. After that is 19 hexes.

There is a slight peculiarity here. 1 hex is a hex. 3 hexes is close to a triangle. 7 hexes is close to a hex. 12 hexes a triangle (5x5x5 triangle but with the 3 vertex hexes cut off). 19 hexes a hex, etc. The reason for this is that like with squares, the space goes from "grid in the middle" to "intersection in the middle" back to "grid in the middle", etc. for each size increase. However, the alternating sizes are like "rounded triangles". Like hexes they are very similarly shaped to a circle and area effects (like for mists) are very easy to draw quickly and properly on the map.
Thank you for answering my question. Also thanks to Sammael for the link.

#### Mouseferatu

##### Hero
Sir Sebastian Hardin said:
Now the area of effect of my 20ft radius Fireball will be SQUARE!!!!!!!!!!!!!!!

I prefer any of the 3.x methods (Eventhough I like almost everything from 4th, btw)

See, this complaint I still don't get.

Your character's not "really" a square, and doesn't "really" occupy a square space. That horse, or that dragon, aren't really squares. That tree isn't really a square. But they're all abstracted to occupy squares on the board.

So why is the fireball any different? It's just another "object" that isn't really a square, but is abstracted to one.

#### Plane Sailing

Mouseferatu said:
But I'll hereby officially concede that, for those for whom such notions are too abstract or break any sense of verisimilitude, hexes are indeed the better bet than any system of squares.

Have you come across "battleboards"? That was the old name for a system with offset rows of squares, and it actually includes in many ways the best elements of squares with the best elements of hexes

It allows orthogonal movement with less shuffling than a hex grid, while allowing 1 movement point per square to make sense in terms of measuring distance.

Cheers

#### Plane Sailing

Mouseferatu said:
So why is the fireball any different? It's just another "object" that isn't really a square, but is abstracted to one.

I guess the 'ball' in fireball makes a bit of a difference!

#### Imban

##### First Post
Mouseferatu said:
See, this complaint I still don't get.

Your character's not "really" a square, and doesn't "really" occupy a square space. That horse, or that dragon, aren't really squares. That tree isn't really a square. But they're all abstracted to occupy squares on the board.

So why is the fireball any different? It's just another "object" that isn't really a square, but is abstracted to one.

It comes down to individual feelings, but... essentially this is a question of minimum granularity versus... something else.

On a map where you're using squares or hexes, the minimum granularity of something is a square or a hex. A sphere or circle has to be abstracted to "as close as we can get, but painted in five-foot squares". Compare early video games and their obviously pixellated graphics, where you could see every pixel: the minimum granularity of something is one pixel, but you can still attempt to draw a circle. It just might not look very circular, having jagged edges and only being a dot or a box or a star at very small sizes.

This is abandoning that attempt altogether, when there are the "resources" available to not. (Plus, it's supposedly losing us cones altogether, according to that latest podcast. That's double lame.)

#### keterys

##### First Post
Sigh

It's curious the things that people react strongly to.

Okay, here's an easy exercise to make it work. Look at your grid map and remember for a moment that it's an abstraction. Now, instead of thinking that the abstraction is 'a diagonal square goes from 1.4 squares to 1, imagine instead that the diagonals are stretched visually from the 1 square they actually are so that instead of a circular grid (which doesn't really work) it's displayed as squares for ease of play.

Okay, now the lengths are correct. Someone 9 squares away is actually always 45 feet away. Thank the Gods of Math.

Disclaimer: Any brain damage caused by actually trying to think through the impact of this 3D space contraction is not the fault of the poster, Wizards of the Coast, or the Far Realms.

P.S. I played with 1=1 for quite a while, back when 3rd edition rules actually worked that way, and the game honestly works better that way. The oddities (square circles, for instance) are quickly gotten past and you have direct savings pretty much every session... and for some players (sigh) _every turn_.

#### keterys

##### First Post
They've used cones in 4E playtests and in the D&D Minis rules. As far as I can tell, 'no cones in 4e' is a rumor.

#### Imban

##### First Post
keterys said:
It's curious the things that people react strongly to.

Okay, here's an easy exercise to make it work. Look at your grid map and remember for a moment that it's an abstraction. Now, instead of thinking that the abstraction is 'a diagonal square goes from 1.4 squares to 1, imagine instead that the diagonals are stretched visually from the 1 square they actually are so that instead of a circular grid (which doesn't really work) it's displayed as squares for ease of play.

Okay, now the lengths are correct. Someone 9 squares away is actually always 45 feet away. Thank the Gods of Math.

Er, uh... ... well, this just results in equilateral right triangles instead of square circles. That's still Far Realm Geometry.

#### keterys

##### First Post
Hmm, apparently I'm explaining poorly. Don't change the math. Change the display. For example, you can display three dimensions on a two dimensional surface. In this case, diagonal distances are just displayed differently.

It does work. It's just not very human. It's fine for describing things though - unless, as noted, you really did think the horse was a 10 foot cube of flesh and the fireballs had jagged blocky angles, already.

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