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

• Autorzy: Prokopová M.
• Konferencja: X Polish-Czech Mathematical School (10 ; 04-07.06.2003 ; Poraj near Częstochowa, Poland)
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Euclidean geometry; phylogenesis; ontogenesis

PL

geometria euklidesowa; filogeneza; ontogeneza

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2003
• Tom: Vol. 9
• Strony: 179--185
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Prokopová M.

• Department of Mathematics, Faculty of Education, J. E. Purkine University, Ústí nad Labem
• Department of Mathematics and Mathematics Education, Faculty of Education, Charles University in Prague

Bibliografia

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