The lattice polygon with vertices (in this order): (0, 0), ( 1,2), (3,1), (2, –1), (0, 0) is convex and simple.
True ; False
True. There are no re-entrant angles or self-intersections.
2.
The lattice polygon with vertices (in this order): (0, 0), (3, 1), (2, –1),
(1, 2), (0, 0) is convex and simple.
True ; False
False. We can think perhaps of vertex (2, –1) moving from position (2, 2), giving a (very) re-entrant angle and intersecting the side joining (0, 0) and (3, 1).
3.
Points A and B belong to set S, and segment AB is contained in S. Therefore S is convex.
True ; False
False. For S to be convex, this argument must hold for all choices of points A and B.
4.
Three examples of a convex set are:
Your answer might include: circle, sphere, triangle, square, rhombus ...
