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(Solved): be sure to give at least a brief explanation or justification for each claim that you make. (1). [5 ...
be sure to give at least a brief explanation or justification for each claim that you make. (1). [5 points] (Refer to Problem 1.16, Devadoss-O'Rourke.) (a). For the polygon below, find the number of distinct triangulations. Show your work, explaining your answer. (b). Draw two different simple polygons
Pand
Q, each having exactly 4 different triangulations, while having different numbers of vertices, convex vertices, and reflex vertices. (i.e.,
n(P)!=n(Q),
c(P)!=c(Q), and
r(P)!=r(Q), where
n(P),c(P), and
r(P)denote the number of vertices, the number of convex vertices, and the number of reflex vertices of polygon
P). State clearly what the values of
n,c, and
rare for each example, and justify (briefly) why they each have exactly 4 different triangulations.
