
20121031, 06:19 PM (ISO 8601)

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#1052
Re: "Wait, that didn't work right"  the Dysfunctional Rules Collection
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 feet^{2}, so Pi = 4
10' radius =12 squares = 300 feet^{2}, so Pi = 3
20' radius = 44 squares = 1100 feet^{2}, so Pi = 2.75
40' radius = 172 squares = 4300 feet^{2}, so Pi = 2.6875
80' radius = 684 squares = 17100 feet^{2}, 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.