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### Is a Star Concave or Convex?

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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.

```

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

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