Explain Like I'm Five: D&D's Pi = 4 Problem

[Fax Celestis]

Someone break it down for me please.

Bonus points for showing what happens if pi is actually 3, 4, or even 5.

[Kornaki]

The definition of pi is the number that makes the formula "Area of a circle = pi*radius^2" work.

If you have a five foot radius blast in DnD, it covers four 5 foot squares. That's 100 square feet, so we have
100 = pi*5^2 = 25*pi
pi = 4.

[Ernir]

This was tackled rather well here. (http://www.giantitp.com/forums/showpost.php?p=14148691&postcount=1052)

[Juntao112]

Someone break it down for me please.

Bonus points for showing what happens if pi is actually 3, 4, or even 5.

The universe explodes.

No, really. (http://en.wikipedia.org/wiki/Einstein_field_equations)

[Fax Celestis]

The universe explodes.

No, really. (http://en.wikipedia.org/wiki/Einstein_field_equations)

I'm five. I understand what "universe explodes" means, but not what all that math means.

[Juntao112]

Since several key physics equations and formulas describing the world and forces need pi to function properly and describe our world, changing pi means throwing all physics out the window. And given that everything from the mass of the proton to the charge of the electron is finely balanced to allow for the formation of matter, this would be disastrous as atoms become unstable and fly apart or collapse on themselves.

[Yuki Akuma]

Pi is a number that tells you the shape of circles (and spheres). If pi was different, circles (and spheres) would be shaped wrong, and things wouldn't fit together properly.

So, because in Dungeons and Dragons the rules imply that pi is 4 (which is wrong), it means that the world of D&D shouldn't fit together properly and shouldn't work.

Alternatively, it means that explosions in the world of D&D make really weird shapes, which is silly.

[Psyren]

Whew, man, what on earth is that sme- Oh right, mounds of dead catgirls. Carry on!

Also, what Kornaki said, though as Yuki pointed out you get some pretty deformed spheres that way too.

[originalginger]

Already explained well enough above, so I will instead offer a simple solution that fixes this, and a number of other distance calculation problems.

Play gridless. My group uses a 3/4 inch = 5 foot scale. We have three measuring sticks made of thin dowels that are painted in alternating colors to show distances of 6 (30 feet) 10 (50 feet) and 20 (100 feet)

We also have templates for circular and cone spells of various ranges made of bent wire.

Quick and easy, fixes the pi=4 issue, ends up making move actions and combat faster increasing the pace of the game, allows much more freedom of movement, and allows maps that don't fit nicely in a grid.

[bekeleven]

Quick and easy, fixes the pi=4 issue, ends up making move actions and combat faster increasing the pace of the game, allows much more freedom of movement, and allows maps that don't fit nicely in a grid.

I bet you enjoy attack of opportunity calculations.

[JaronK]

Eh, Mordheim is played that way just fine. You just have to chose your engagement radius (in inches or centimeters).

And the fact is, pi is always ~3.14159. It's just that circles in D&D are actually chunks of squares.

JaronK

[skyth]

The definition of pi is the number that makes the formula "Area of a circle = pi*radius^2" work.

If you have a five foot radius blast in DnD, it covers four 5 foot squares. That's 100 square feet, so we have
100 = pi*5^2 = 25*pi
pi = 4.

But for a 10' blast, it covers 12 squares, which is 300 square feet, thus pi=3 :)

[originalginger]

I bet you enjoy attack of opportunity calculations.

Honestly, we have been playing that way for so long that we rarely actually measure, we just kinda eyeball it unless there is a dispute on a borderline distance. The circular spell range templates are useful for determining threatened area for opportunity attacks, who is considered adjacent to who, and other such calculations. Even if there is a dispute, I usually just give the PCs the benefit on a borderline case.

[Psyren]

I bet you enjoy attack of opportunity calculations.

And flanking and cover and LoE and...

[NeoPhoenix0]

Most of the stuff that has been said is true, except in dnd pi is always 4. This is because of the grid system. Pi is not defined by the equation A=pi*r^2, it is actually defined by the equation C=pi*d, the ratio between the length circumference (or perimeter) and the length of the diameter (or distance across the center). The equation for area is just wrong in dnd because the physics in dnd cause all area effects to become blocky.

This isn't quite right either though since the shape area effects take is never an actual circle. In dnd any effect with a radius does not follow the rules for anything pi can normally be applied to.

tl;dr/lesson: Don't apply pi to radius based area effects, they don't take the shape of a circle.

Edit: obviously scholars don't learn about pi in dnd because it never comes up. The main people who know about pi would be architects and the various artists that make all the circular objects in the world. Even they might not have any reason to learn it.

[originalginger]

And flanking and cover and LoE and...

Flanking, if the flankers are more or less on opposite sides of the target and within a few feet, then they are flanking, if not they aren't

Cover, either you are behind something that gives cover or you aren't, and either that cover is partial or full over. Kinda just context and common sense.

LoS, LoE, basically same idea as cover. Either there is something blocking your sight, spell, arrow, whatever, or there isn't. The measuing sticks are useful here fo determining a straight line, if from your token/mini to the target intersects something, than LoE and LoS are blocked.

I admit it takes a bit of fudging, but it actually allows you ignore a lot of the nit-picky rules and just kinda do it.

[Psyren]

I admit it takes a bit of fudging, but it actually allows you ignore a lot of the nit-picky rules and just kinda do it.

If it works for your group that is what matters. I prefer bright line tests myself; to each his own.

[originalginger]

Yeah, by-the-book players would probably hate it, but we have been playing together for quite a long time, and no one is interested in cheating, but we are interested in avoiding spending time looking up obscure rules, disputing ambiguous rules, or otherwise holding up the game. The players know I am a fair DM, and I know they are honest players, so the "screw-it-and-do-it" method works well for us. And our pi=3.14, which is nice.

But this is rather off topic for the thread, and I have said my piece.

[NeoPhoenix0]

My personal favorite fix is hexes. It's not perfect, but it fixes a lot of problems found with a square grid.

[Chronos]

A hex grid is better than a poorly-implemented square grid, but worse than a well-implemented square grid. In a perfect system, a circle would be represented by a circle. In a poorly-implemented square grid system, a circle is represented by a square. In a hex grid system, a circle is represented by a hexagon, which is a better approximation of a circle than a square is. In a well-implemented square grid system, a circle is represented by an octagon, which is a better approximation than a hexagon. D&D, thanks to the "diagonals count as one and a half" rule, is a well-implemented square grid system.

This superiority of a square grid over a hex grid is made all the larger by the fact that many D&D environments (including almost all artificial ones) are actually laid out according to a square grid. Any representation of, say, a square room in a hex grid is going to be clunky.

[Yogibear41]

Basics:

Our universe Pi is approximately 3.14 and physics work the way they do


DnDs Universe Pi = 4 and magic, monsters, and dragon-wrought Kobolds exist

[sketchtb]

We use a hex grid for larger scale maps to figure out travelling, square grids for encounters... Seemed logical when we started.