Is a Star Concave or Convex?Date: 4/2/96 at 5:59:49 From: Anonymous Subject: Star-shaped polygons Hello, As far as what I understand about convex and concave polygons, a star-shaped polygon must be a concave polygon. However I have come across a book which says that a star-shaped polygon is convex. Can you please clear my doubt? Thanks. madhavi Date: 4/3/96 at 12:21:25 From: Doctor Ken Subject: Re: Star-shaped polygons Hello! I think I know what might be leading to your confusion. There are actually two notions that people talk about. One is "convex," which is what Doctor Jodi told you about. The other is "star convex," which is a different property altogether. Star convex means that there is some point (think of it as one in the center of your star shape) such that you can connect this point to every other point in the figure by a straight line segment that lies entirely in the figure. So it's pretty obvious that a star is star convex, but it's not convex. Want an example of a shape that's not star convex either? How about the inside of a doughnut? Or in two dimensions, the region between two concentric circles (this region is called an annulus). -Doctor Ken, The Math Forum |
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