Concave and Convex Polygons

Date: 08/13/2001 at 23:51:01
From: Jack 
Subject: Convex and Concave

What's the difference between convex and concave polygons (or shapes 
in general)?

Thank you very much.

Date: 08/14/2001 at 12:01:10
From: Doctor Peterson
Subject: Re: Convex and Concave

Hi, Jack.

A concave figure is one that has an indentation. 

This can be stated precisely by considering all line segments joining 
any two points in the interior of the figure. If the entire segment 
always lies within the figure, then the figure is convex; but if you 
can go on a straight line from one point in the interior to another 
and pass outside of the boundary, then the figure is concave:

             +---------------------+
            /                       \
           /                         \
          /                           \
         /                             \
        /                        +      \
       /                        /        \
      +                        /          \
       \                  +----------------+
        \                  \ /
         \                  \
          \                / \
           \              /   \
            \            +     \
             \                  \
              +------------------+

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/