Hexagon Math Challenge

[Legend]

In another thread... http://www.bgforums.com/forums/viewtopic.php?p=44620 the topic came up regarding hex size so I thought I would start a thread about the math concerning our hexes found in the game. I'm hoping to see some interesting posts (with pictures if possible) relating to the size of hexes and the math behind it all.

Some questions I have are as follows:
- what is the area of a hex?
- how do you calculate the area?
- how many hexes can an E3 see - or look into (350km spotting range) - with a 15km hex size?
- with a hex distance of 5 km vs 10 km vs 15 km, how many hexes would the above E3 have to look into?
- are there any other hex questions?

[haenkie]

Just draw a cube around it and subtract the 4 triangles.

And as a hexagon all the distances are he same, so 350/15=23+1 because of the round down factor.

[Draken]

Area of a regular hexagon:


where "a" is the lenght of one side....

Question:

When ypu say that the size of the hex is X km, what do you mean? Is it the distance from the center to one of the vertices? Or is it from one vertice to the opposite one? I always had assume the last one, but it would be nice an official answer

[Legend]

Hex "distance" is in fact the length from one side to the other. It is were a circle it would be the "diameter".

So, how many hexes are in a 350 spotting range (radius) with a 5km hex size, 10km, 15km? Any takers?

[Lightbringer]

where did I put that hex graph paper and my old compass...

(thanks for the clarification on wether hex size was a radius or a diameter)

[Draken]

So, how many hexes are in a 350 spotting range (radius) with a 5km hex size, 10km, 15km? Any takers?

Assuming that all units have the same relative position to the center of the ehx they are in:

The spotting radius will be 70 , 35 and 23 hexes respectivately (rounding to the closest integer number), so (again rounding to the closest integer and using only 6 decimals for PI) , the E3 will see an area of 15394, 3848 and 1662 hexes respectivately