The Importance of Geometry ConstructionsDate: 12/29/98 at 21:46:10 From: kel Subject: Geometry constructions I am doing a report on constructions in geometry. I would like to know why constructions are important. I realize that they challenge us to use different tools but there must be more to it then that. So I was wondering if you could give me more of a reason why constructions are so important? Thank you very much. Date: 12/30/98 at 12:26:56 From: Doctor Peterson Subject: Re: Geometry constructions Hi, Kel. That's a good question. We tend to teach it out of tradition, and forget to think about why it's worth doing! Certainly learning how to use the tools is useful. Some of the techniques are useful in construction (of buildings, furniture, and so on), though in fact sometimes there are simpler techniques builders use that we forget to teach. But I think the main reason for learning constructions is their close connection to axiomatic logic. If you haven't heard that term, I'm talking about the whole idea of proofs and careful thinking that we often use geometry to teach. Euclid, the Greek mathematician who wrote the geometry text used for centuries, stated many of his theorems in terms of constructions. His axioms are closely related to the tools he used for construction. Just as axioms and postulates let us prove everything with a minimum of assumptions, a compass and straightedge let us construct everything precisely with a minimum of tools. There are no approximations, no guesses. So the skills you need to figure out how to construct, say, a square without a protractor, are closely related to the thinking skills you need to prove theorems about squares. You may be interested in looking at Euclid's theorems to see for yourself how much involves constructions. Here's a Web site by David Joyce of Clark University on Euclid's first book, the first proposition of which is a construction: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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