Over on another thread we noticed that the values of Pi, calculated by the area method, for circular spell templates was very wrong. Now there will be some inaccuracy, but as the radius increases then the value should approach 3.14....

5' radius = 4 squares = 100 feet2, so Pi = 4
10' radius =12 squares = 300 feet2, so Pi = 3
20' radius = 44 squares = 1100 feet2, so Pi = 2.75
40' radius = 172 squares = 4300 feet2, so Pi = 2.6875
80' radius = 684 squares = 17100 feet2, so Pi = 2.671875

The value of Pi is too small, and the divergence increases.

If you actually take a pair of compasses and draw a circle on squared paper it is readily apparent that the templates are rounded incorrectly.

Consider the 20' radius

WotC template

OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO

44 squares, Pi = 2.75

More accurate template

OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO
OOOOOOOO

52 squares, Pi = 3.25.