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The number of operations needed to effect a Geometric Construction as determined in Geometrography. If the number of operations of the five Geometrographic types 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 $m_1S_1+m_2S_2+n_1C_1+n_2C_2+n_3C_3$. It is apparently an unsolved problem to determine if a given Geometric Construction is of smallest possible simplicity.

See also Geometric Construction, Geometrography


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, 1976.

© 1996-9 Eric W. Weisstein