It happened one day that I had some GURPS books while on a bus on the way to an airport, and whilst comparing the areas of effect of Regular and Area spells. While pondering the tiny chart on the sidebar of p. M 10 and p. B 150, a mathematical pattern lept out at me.

Here is what I found:

n

1 = 1

2 = 1 + 6

3 = 1 + 6 + 12

4 = 1 + 6 + 12 + 18

Using a piece of grid paper, I then verified the above and was pleased to find the following result:

5 = 1 + 6 + 12 + 18 + 24

avg = m(m+1)/2

Substituting:

6 (n-1)(n)/2 + 1

3n(n-1) + 1

3n*n -3n + 1

Since the "Height" of a magic hex is defined as 12', we know that each hex contains 3x3x12 = ~100cf, calculated exactly as 85cf (see p. TM37). Reverse engineered, one gets 7.08sf/hex.

Combine this with a table of densities, and now one has a dangerous combination.

e.g.: Create Earth, 10 hex radius: 3×10×10 - 3×10 + 1 => 300-30+1 => 271 hexes.

271 hexes × 85cf/hex = 23,035cf.

23,035cf × 100lbs/cf (dry sand) = 2,303,500lbs -> ~1,120 tons (great fun indoors!

A subsequent casting of Earth to Stone would double its mass (similar to concrete)...

To tell how many hexes one has to play with as per the GURPS FAQ.

Another use:

http://www.krommnotes.org/krommmag.html

"Q: Can the shape of the area be changed for Area spells? That is if you cast a 2 hex area spell can you stretch it to 1 by 7 hexes? (a)"

The answer was yes!

(based on public domain hex grid found here)