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CTK Exchange
JJ
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Jul-12-08, 05:14 AM (EST) |
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1. "RE: trisection of an angle"
In response to message #0
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The catch is that they are neusis constructions.
Exact trisecting of angle with compas and straightedge only is well-known. There are may ways to do it. What is impossible is trisecting with compas and straightedge only AND complying with the Ancient Greek rules. If the rules are not strictly respected, the construction is a neusis construction.
Some typical examples of constructions, some rough, some exact but neusis, are reviewed in the paper "Trisection.doc" available through :
https://les-mathematiques.u-strasbg.fr/phorum5/read.php?8,410762,410967#msg-410967
Abstract :
The problem of dividing an arbitrary angle into three equal angles, using only compas and straightedge, is one of the famous geometric problems of Antiquity. Although such a construction has proved impossible when fully complying with the Ancient Greek rules, some people are not yet convinced and still searching. For their benefit, a range of very simple and often clever trisection methods is reviewed. As a matter of fact, these constructions are not exact but only approximative, although the deviation can be reduced to one's will and considered as not significant in practice. One will not find any more theoretically exact solutions to this ancient issue than neusis constructions. |
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