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Is a Star Concave or Convex?

Date: 4/2/96 at 5:59:49
From: Anonymous
Subject: Star-shaped polygons


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?



Date: 4/3/96 at 12:21:25
From: Doctor Ken
Subject: Re: Star-shaped polygons


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

Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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