Pick's Theorem -- Page 10


Did you? I would not think so. But we can make some progress if we sort the table, first by boundary dots.

FigureFGHIJLKABCDENM
boundary
dots
 3  3  4  4   4  5   6  10  10  10  11  12  12  18 
interior
dots
00012002343350
Area0.50.51231.526787.58108

Look especially at the number of boundary dots that are repeating, 4 and 10. What happens when we have the same number of boundary dots but the number of interior dots increases?

If the number of boundary dots stays the same but the number of interior dots increases by 1 the area increases by
 0
 0.5
 1
 No clear pattern

CONTINUE