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We are allowed to assume that any polygon, convex or not, can
be split into a finite number of non-overlapping triangles.
However in this proof we assume that the interior of the
polygon does not have any holes like the red polygon shown with a
yellow hole in the diagram. Pick's formula is related to Euler's
formula and ${\rm area }(P) = i + {1\over 2}p - q$ where $q$
depends on the number of holes.
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A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?