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 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

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.