So when measuring distance with a hexagon map the distance of side-to-side, height and diagonally are all different. I can use a online calculator to determine the differences. What I don't understand is why they look the same. On my maps the side-to-side measurement I have always assumed measurements are made at the far center joints of the hexagon is 48 miles but I suspect this is incorrect.
According to the online calculate the height is 83.13844 miles and diagonally equals 96 miles. The distance all look about the same. When I measure a hexagon with a ruler I get nothing even close to what the online calculator tells me.
Why the difference? Please keep your answer as simple as possible, if you incorporate a bunch of math calculations I won't understand it anyway.
Also I was wondering with this hexagon scale issue, what the miles were for my world.
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The point of using hex maps is that, measuring center to center, a route drawn across a map can be decently approximated just going hex to hex. It will not be exact, of course, but it is easy to calculate. If you want true straight line distances, squares are far easier to count.
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It's not always clear to me what you mean by terms like "side-to-side", "height", "diagonally", and "far center joint" so let me draw a picture here. With that diagram, maybe we can establish a common terminology. There's a regular hexagon. Now let's draw a line segment perpendicular to line segment df from point a to point e, such that it bisects the hexagon; in other words, de = ef. So one hex equals the distance from a to e. And let's draw another line segment from point d (one corner of the hex) to point b (the opposite corner of the hex).
Now... triangle cde is your classic 30-degree / 60-degree / 90-degree triangle, so the ratios of the sides of that triangle are well-known. You can Google it if you don't believe me.
So if, as I said, the distance from a to e is 1 hex, then the distance from c to e is obviously 1/2. Therefore, the distance from c to d is 1 / sqrt(3). So it follows that the distance from b to d is 2 / sqrt(3). And the distance from d to e is 1 / (2 (sqrt(3)), so the distance from d to f is 1 / sqrt(3).
So let's say in your map 1 hex = 48 miles. So ae = 48 miles. bd = about 55 miles. df = about 28 miles.
Does that help?
EDIT: After I posted this, I found a mistake in my calculation and corrected it. But my error has humbled me enough that I must admit that I am prone to mistakes. Therefore, I'm leaving my reasoning in my post. In other words, EileenProphetofIstus, I heard you say "if you incorporate a bunch of math calculations I won't understand it anyway" but I'm leaving those calculations there so that anyone may challenge my math. In fact, Paizo posters, please do check and challenge my math.
Usually, if a hexagon is said to be 48 miles across, that's the difference between any two parallel sides - the distance ae in Aaron Bitman's picture. The distance between opposite points is different. The distances may look the same to you, but they are different. Ultimately the point-to-point distance doesn't matter when using a hex map.
As Sissyl said, just count hexes along the route, multiply by 48 (or whatever is the size of your hex) and voila, you have the approximate length of the route in miles.
What I have always done is take the mile measurement for the hex, in this case 1 hex = 48 miles and assumed that if the PCs pass through one end of the hex and exit one that is directly across it, the distance travelled was 48 miles.
I just did some investigating and if I understand the geometry correctly "side to side" as mentioned in the online calculator seems to be one side of a hex, in other words one single line of the hex. Now if this one line is 48 miles and another line of the same distance was drawn from the top of the hex towards the center, it should end in the middle of the hex. It would take two such lines to go from the top of the hex to the bottom of the hex. At 48 miles per line(or side) that would be the 96 miles I get from the online calculator.
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If you measure from the exact center of one hex to the exact center of an adjacent hex, it will be 48 miles.
IF you measure the distance from the middle of one side of a hex to the middle of the opposite side (in a straight line) it will be 48 miles.
Measuring 'side-to-side' on a hexagon is just like measuring from side-to-side on a square or a rectangle. You choose a side and measure across the figure to the 'other' (opposite) side. Side-to-side is a very different measure from 'corner to corner', which is what you do if you measure from one point on the hexagram across to the opposite point.
The number you need to use in the calculator is 24 miles for the "in-circle radius". On Aaron's diagram that is the CA or CE length. The distance between A and E is 48 miles.
The length of the side is 27.7 miles (roughly) The side (one line) is not 48 miles, it is approximately 28 miles.
I'm having a hard time understanding exactly how you're using the hex grid, EileenProphetofIstus. You're using the hex lines to measure your distance?
One thing to keep in mind is that hexes are more convenient for some things, less for others. They're great for tactical movement on smaller scales because they avoid the alternate diagonals problem of squares and for drawing things like fireballs and other burst radiuses. They're not so good for drawing corridors that meet at right angles.
When you use them for macro-scale movement like overland travel, you ultimately use them just like square grids... if you think of them in the right context. Think of them as measuring the distance from one point in the hex to about the same point in another hex. That's basically using the width of the whole hex from one side to the side directly opposite or center to center. Let's call that the "span" of the hex. You do that with squares too, ultimately. But squares have the advantage of that span distance being exactly the same as the line segments that make up the sides of the square. So with squares, you can use the line segments along the side or the span from one side to the other interchangeably. You can't do that with hexes because their sides don't match the span of the hex.
When a hex says it's 48 miles, that means the span from one side to the opposite side is 48 miles. If you measure things in hexes by focusing on the span center to center, one side to opposite side, you'll find them easier to understand and use.
ok thanks
Yep, A to E. Not B to D.
If some spoilsport insists on traveling corner to corner, ignore the difference like you ignore a half hit point.
Seven circles? Yes.
I would say you need five at least to get the last distances right...?
Remove the straight line and you need more than three.
Just did the source code for drawing hexagons in computer programs. Is anyone interested?Guess not.
Try Here.
http://chat.dmtools.org/
no just three
here's a long sort of videos, but you get the idea
Thanks for the video link.
I wish he'd proved that the top and bottom sides were equal in length to the other four. They are, I just wish he'd spoken about it. Feels kind of 'almost finished'. :/
Yeah. He just didn't prove it was a regular hexagon, that's all.
He doesn't need any further circles to prove that, but it just would have been nice to have finished off the argument, rather than just joining the dots for the last two sides.
