Pick's Theorem -- Page 11


Yes, if the number of boundary points is the same but the number of interior points increases by 1.

Now we sort the chart by interior points.

FigureFGHLKMIJABDECN
boundary
dots
 3  3  4  5  6  18   4  4  10  10  11  12  10  12 
interior
dots
00000012233345
Area0.50.511.52823677.58810

Now inspecting the table, especially columns G,H,L,K and B,D,E a pattern becomes apparent.

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

CONTINUE