Geometric ProofsDate: 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/ |
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