Geometric Proofs

Date: 11/28/98 at 11:48:34
From: Anne Haggarty
Subject: Geometric proofs

I am trying to help a friend learn geometric proofs. I took the course 
last year but I need a straightfoward way to explain things to her. 
Do you have any suggestions?

Date: 11/28/98 at 13:14:00
From: Doctor Jaffee
Subject: Re: Geometric proofs

Hi Anne,

The best advice I can give you is this. There are three preliminary 
steps required to construct a good proof.

   The first is to understand and be aware of the definitions of each   
   of the terms associated with what you are trying to prove.

   Second, know and understand previous proven theorems related to what 
   you are trying to prove. Some of these theorems will be relevant; 
   some won't.

   Third, know the basic rules of logic.

Now, these are fairly straightforward. The next step is a little 
trickier, however. What you want to do now is combine what you know of 
the relevant definitions and theorems using the logic to construct an 
acceptable proof. The proof may be in the traditional two-column 
format, it may be a paragraph, and it could even be a good diagram with 
the appropriate commentary.  

Most people learn how to do this by reading proofs that other 
mathematicians have constructed, practicing on simple proofs, and 
eventually graduating to more and more complicated proofs. Exceptional 
students can devise original proofs of theorems for which they have not 
seen other proofs.

I hope these suggestions have been helpful. Write back when you have 
other questions. Good luck.

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