One- and Two-sided Polygons

Date: 12/07/1999 at 15:56:45
From: Sue
Subject: Polygons

Dr. Math:

You said that there are such things as monogons and digons - one-sided 
and two-sided polygons. What are they? None of my math teachers has 
heard of them. Please write back with a little diagram of each.

Thank you.

Date: 12/07/1999 at 16:13:32
From: Doctor Rob
Subject: Re: Polygons

Thanks for writing to Ask Dr. Math, Sue.

Since there is no such thing, it would be really hard to draw a 
diagram of either. The names are constructed by analogy with names of 
figures with more sides. Mono- means one, Di- means two, and Octa- 
means 8. Thus Octagon for an 8-sided figure would correspond to Digon 
for a 2-sided one (if it existed) or Monogon for a 1-sided one (if it 
existed). 

Actually, on the surface of a sphere, you *can* have such figures: a 
monogon is a hemisphere, and a digon is a spherical lune (see

  http://mathforum.org/dr.math/faq/formulas/faq.sphere.html#lune   

for pictures). Of course you have to replace straight lines with great 
circles on the sphere for the sides, but that is standard practice in 
spherical geometry and trigonometry.

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