Journal for Geometry and Graphics 14 (2010), No. 1, 015--028
Copyright Heldermann Verlag 2010
Two Approaches to Geometrography
Jorma K. Merikoski
Dept. of Mathematics and Statistics, University of Tampere, 33014 Tampere, Finland
School of Applied Educational Science and Teacher Education, University of Eastern Finland, 57101 Savonlinna, Finland
Geometrography studies the complexity of ruler-and-compass constructions. According to our knowledge, so far the only remarkable work in this field is by É. Lemoine. We survey his method and present another method based on statistical modelling. We compare these methods by studying the complexity of certain constructions of a perpendicular to a line and a regular pentagon. A purpose of this paper is to show that geometrography has potential to enrich geometry and graphics education in school. The latter, statistical, method also provides tools for a more advanced analysis of error propagation through geometric transformation.
Keywords: Geometric constructions, complexity, statistical modelling.
[ Fulltext-pdf (252 KB)] for subscribers only.