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单词 Geometrography
释义

Geometrography

A quantitative measure of the simplicity of a Geometric Construction which reduces geometric constructions to five steps. It was devised by È. Lemoine.

Place a Straightedge's Edge through a given Point,

Draw a straight Line,

Place a Point of a Compass on a given Point,

Place a Point of a Compass on an indeterminate Point on a Line,

Draw a Circle.

Geometrography seeks to reduce the number of operations (called the ``Simplicity'') needed to effect a construction.If the number of the above operations are denoted , , , , and , respectively, then theSimplicity is and the symbol is .It is apparently an unsolved problem to determine if a given GeometricConstruction is of the smallest possible simplicity.

See also Simplicity


References

De Temple, D. W. ``Carlyle Circles and the Lemoine Simplicity of Polygonal Constructions.'' Amer. Math. Monthly 98, 97-108, 1991.

Eves, H. An Introduction to the History of Mathematics, 6th ed. New York: Holt, Rinehart, and Winston, 1990.


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