Why So Many Shapes?

Date: 05/01/2001 at 21:42:52
From: Yifeng Zhao
Subject: Why so many shapes?

Dear Dr. Math,

I just want to know why there are so many shapes in the world. I'm 
trying to figure it out, but when I tried, I thought it's impossible.

Date: 05/02/2001 at 13:58:29
From: Doctor Ian
Subject: Re: Why so many shapes?

Hi Yifeng, 

That's a good question. Here's one way to think about it. If I give 
you a number greater than 2, you can think of a shape that has that 
number of sides, right?

  Number    Shape
  ------    -----
    3       triangle
    4       rectangle
    5       pentagon
    6       hexagon
    7       heptagon
    8       octagon
    
and so on.  You can find names for lots of these shapes in the Dr. 
Math FAQ, at

  Naming Polygons and Polyhedra
  http://mathforum.org/dr.math/faq/faq.polygon.names.html   

but even if you don't know the 'official' name, you could use a name 
like '256-gon' or '4527657-gon', and someone else would know what 
you're talking about. 

Since every number has at least one shape associated with it, there
must be as many shapes as there are numbers. But there is an endless 
supply of numbers - so there must be an endless supply of shapes, too!  

Does this help?  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

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

Date: 05/07/2001 at 14:13:14
From: Yifeng Zhao
Subject: Re: Why so many shapes?

Dear Dr.Math,

I didn't expect to get your answer this quickly. Thank you for your 
patience and intelligent hard work! I will devote more time to 
learning about math, and of course Ask Dr. Math.

Best regards,

Yifeng