Rotating area bursts to be off-grid

[Ketjak]

Geometrically speaking, a circle is defined as the set of points that are a certain distance from a center point. An area burst N is circular - it includes all squares that are N or fewer squares away from the origin square.

In 4e battle-grid geometry, all circles are also squares, but not all squares are circles. An area burst is fundamentally defined as being circular (in the equidistant sense). If you rotate the square, it ceases being a circle.

Encourage your player to look into feats like Enlarge Spell and War Wizardry, and items like Architect's Staff.

This time, McCoy squared the circle.

 

[shamsael]

pi is 4, not 3...

and its not crazy... it is just using the infinite norm... we learned it in our 1st or second linear algebra lesson... oh wait it IS crazy^^

My bad. I was thinking in terms of diameter->area but goofed on the formula

The area of a circle in 4e happens to be diameter squared.

Also, depending on how you interpret the geometry, the equation for circumference may vary. If you take the circumference of a burst 1 to be the some of the lengths of the edges of the squares, then the circumference is 12, making pi 4.

If you instead take the circumference to be the number of squares one walks to trace the circle (it's impossible to stand on the edge of a square), then a burst 1 either has circumference 8 OR circumference 12.

Burst | Diamter | Circumference A | Circumference B
1 | 3 | 8 | 16
2 | 5 | 16 | 24
3 | 7 | 24 | 32
x | d=2x+1| A=pi*d-4 | A=pi*d+4