Convex and Concave Polygons

Date: 3/23/96 at 2:17:26
From: Anonymous
Subject: convex and concave polygons

Can you please answer this question of mine?

What are convex and concave polygons?

Thanks,
madhavi

Date: 3/30/96 at 3:46:1
From: Doctor Jodi
Subject: Re: convex and concave polygons

Hi there!

Probably most of the polygons you know are convex.  They're 
the ones that geometry classes usually talk about.  Squares, 
trapezoids, rhombuses, rectangles, triangles are all convex, 
because any line you draw from one vertice to another in the 
polygon is on a side or inside the polygon.

A concave polygon is one that is "caved in" a little bit.  This is 
NOT a very good drawing, but maybe it will help a bit
          
  */////////*
  |         /
  |        /
  |       *          
  |        \
  */////////*

See the *'s?  Those are supposed to be the vertices.  You can see 
on the left side that the two vertices are connected by a side, just 
as they would be in a convex polygon.  But on the other side, you 
can connect two of the vertices in a line OUTSIDE the polygon.  
That makes this polygon concave.

I hope this makes sense.  Write back if you have other questions!

-Doctor Jodi,  The Math Forum