Area of a Hex: WHY?

[Ximenez]

So I noticed a statement (in 5th ed., I will note) that for purposes of area, a hex is measured as 2m from point to point, and started using that as the basis for my buildings and such. But...characters move 2m from center to center, which means that 2m would most logically be measured from side to side. Because of this discrepancy, hexes are exactly 25% smaller in area than it seems like they should be. Is there a reason for this? Is it an oversight?

 

And if this seems like a picky question--hey, it's HERO. Wouldn't you expect someone to do the math?

[Ndreare]

I think you are missing something. Hexes are hexagons they are perfect polygons and measuring from any point within a hexagon to a relative point in an adjoining hexagon will always reveal a result equal to the measure of opposing sides of the hexagon.

Circles are deliberately not used because then you would have a lot of empty space.

 

when playing in the theater of your mind it does not matter, but when using maps having hexes works better than anything else.

[Beast]

It also gives more options for doing easy figuring for more angles

squares give 45 and 90

hexes give 15,30 ,45 ,60,75 and 90 degrees

[Old Man]

So I noticed a statement (in 5th ed., I will note) that for purposes of area, a hex is measured as 2m from point to point, and started using that as the basis for my buildings and such. But...characters move 2m from center to center, which means that 2m would most logically be measured from side to side. Because of this discrepancy, hexes are exactly 25% smaller in area than it seems like they should be. Is there a reason for this? Is it an oversight?

 

And if this seems like a picky question--hey, it's HERO. Wouldn't you expect someone to do the math?

 

Sounds like an oversight to me.  Probably not caught until now because only you have attempted to do the math. 

 

(Seriously I don't think I've ever attempted to really define a base or building in Hero terms.)

[Chris Goodwin]

The only way I can see it working out is if you measure it the same way you move.  Otherwise, somehow Area of Effect and movement are calculated totally differently.  

 

In the real world, in math, the area of a hexagon is measured from corner to corner, and the radius refers to the distance from the center point to the corner.  The distance from the center point to the center of a side is called the apothem, which is a word I never knew until I looked it up for a similar discussion elsewhere.

[Ximenez]

OK, I'm asking Steve Long.

[Rebar]

A hex is 2m across. A hex is 2m from centre to centre.

 

Sorry, what exactly is the discrepancy?

 

Are you talking about calculating the area? well, everything in HG is rounded to easy-to-calculate numbers (people are 2m tall, weigh 100kg, semo-log scale of weight is rounded)

[Ximenez]

I am talking about calculating the area. The thing is, neither way produces a convenient number.

[Greywind]

Draw your maps as if they are real buildings. When you are done, lay a clear hex mat on top of it. Instant no-headache.

[Hyper-Man]

I don't understand the problem.

 

The area of an individual hex is covered by the formula in this link:

http://www.drking.org.uk/hexagons/misc/area.html

 

The statement "a hex is measured as 2m from point to point" is absolutely correct if you define the width of a hex from side to side as 2m.  Here is a hexmap with centerpoints that might help illustrate - http://gombe.org/hexmap16x16.gif

 

A hexmap is useful to determine distance for character movement and AOE attacks but is never going to be the best tool for determining the area of a RECTANGULAR region on the map.  L x W is always going to be an easier calculation in that case.

 

Greywind's hexmap overlay is probably the simpliest method to answer the question "How many hexes will fit into the area of building X?"

[bigbywolfe]

I think the OP is confusing the term "points" with "corners".

[TheRealDeal]

Point to Point means center of 1 Hex to the center of the other Hex.

Thus, it means from the center of a Hex to the edge (a perpendicular bisector) is 1 meter. This is called the apothem. The triangle formed is then a 30-60-90 and this means that the side opposite the central Hex angle is 1/root(3) or root(3)/3. The area of the triangle is 1/2bh or 1/2(root(3)/3) x (1) = root(3)/6. There are 12 such triangles in a Hex so the total Hex area is 12 x root(3)/6 = 2xroot(3) or about 3.464 or perhaps just simply 3.5 square meters.

[Ximenez]

The 5th edition rules are very explicit that 2m is the distance from corner to corner, so that the area of a hex should be 2.6m, even though it shouldn't. The key point, though, is that there isn't any particular reason it was done that way, so I can do what I want without unbalancing anything.

[Greywind]

 

Hex: A standard unit of measurement in the game

— a six-sided area one inch (25mm) across on a

map, representing an area 2 meters across (approximately

6.5 feet) in the game setting. Hexes are used

to measure range, movement, and areas in the

HERO System. (Solely for purposes of calculating

the square footage of a building or the like, consider

hexes to be measured from corner to corner.)

 

 

Movement and maps in the HERO System use

hex-shaped inches which, despite their name, are 2

meters (approximately 6.5 feet) wide. Th e text oft en

refers to “hexes” or “inches” interchangeably. Inches

are written 1”, 2”, and so forth

[dmjalund]

I always thought 2m was the distance from one side to another, that's why travelling along a line of hexes could be converted into meters

[Greywind]

Yes. 2m whether from side to side or center to center of another hex.

[Chris Goodwin]

I can't ever remember, in all the time I've been playing HERO System, the area of a hex mattering.  The area of a hex is "one hex".  There's nothing in editions 3 through 5 (I can't speak to 1 and 2 because I don't have them) where it matters whether a hex is 2.6 something or 3.2 something square meters.  

 

(Fun fact: everything is measured from the center of the hex, so technically "Area Of Effect: 2 hex radius" is a single hexagon plus the hexagons immediately surrounding it, making it 3 hexes across, for an actual radius of 1.5 hexes.  Edited to add:  And I just checked it out; if you consider it to be from center point to center point, you're losing half a hex on each side, or one full meter, so you're looking at a circle of 2 meters.  I think that the next time I run any other edition I'm going to go gridless, multiply the hex values by 2, and call them meters.)