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Geometric Constructions - Mathematical and Statistical ...

Geometric ConstructionsPhilosophy of ConstructionsConstructions using compass and straightedge have a long history in Euclidean geometry. Their use reflects the basic axioms of this system. However, the stipulation that these be the only tools used in a construction is artificial and only has meaning if one views the process of construction as an application of logic. In other words, this is not a practical subject, if one is interested in constructing a geometrical object there is no reason to limit oneself as to which tools to use. Philosophy of Constructions The value of studying these Constructions lies in the rich supply of problems that can be posed in this way. It is important that one be able to analyze a construction to see why it works.

two arms with a central pivot. Should you pick up a divider, the arms will collapse, so it is impossible to use them to transfer lengths from one area to another. Modern compasses remain open when picked up, so such transfers are possible. Given the difference in the two tools, it appears that the modern compass is a more powerful instrument,

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