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Students’ Conception of a Point and its Relation to a Straght Line : A Comparison of Phylogenesis and Ontogenesis

Prokopová M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

179--185

A point and a straight line are fundamental objects of Euclidean geometry which is taught at basic and secondary schools. Philosophers meditated on the nature of a point and a straight line long before Euclid (from the 6th century BC). But it was Euclid (about 325-265 BC) who delimited the concept of a point and a straight line (and others) in the First book of his Elements (Stocheia) by means of a definition. The phylogenesis of a point and its relation to a straight line is marked out by names such as Viéte, Kepler, Leibniz, Newton, Bolzano and Cantor. Students meet the concept of a point before they start to create their geometrical structures. Our analysis will try to show that there is a strong parallel between the ontogenetic and phylogenetic aspects of the conception of a point and its relation to a straight line, a ray and/or a segment.