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Geometrography


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

S_1 Place a straightedge's graph edge through a given point,

S_2 Draw a straight line,

C_1 Place a point of a compass on a given point,

C_2 Place a point of a compass on an indeterminate point on a line,

C_3 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 m_1, m_2, n_1, n_2, and n_3, respectively, then the simplicity is m_1+m_2+n_1+n_2+n_3 and the symbol is m_1S_1+m_2S_2+n_1C_1+n_2C_2+n_3C_3. It is apparently an unsolved problem to determine if a given geometric construction is of the smallest possible simplicity.


See also

Simplicity

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References

DeTemple, 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.

Referenced on Wolfram|Alpha

Geometrography

Cite this as:

Weisstein, Eric W. "Geometrography." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Geometrography.html

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