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X Polish-Czech Mathematical School (10 ; 04-07.06.2003 ; Poraj near Częstochowa, Poland)
Języki publikacji
Abstrakty
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.
Rocznik
Tom
Strony
179--185
Opis fizyczny
Bibliogr. 13 poz., rys.
Twórcy
autor
- 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
- [1] M. Bečvářová, Eukleidovy Základy. Jejich vydání a překlady). Prometheus, Praha 2002.
- [2] J. Drábek, Démokritova atomistická metoda. In: Sborník Matematik: v proměnách věku I. Prometheus, Praha 1998.
- [3] P. Eisenmann, Point, segment, line-secondary school pupil's ideas. In: 18 th Czech-Polish Mathematical School. Acta Universitatis Purkynianae. Ústí n.L. 2001.
- [4] P. Eisenmann, Propedeutika infinitesimílního počtu. Acta Universitatis Purkynianae. Ústí n. L. 2002.
- [5] M. Hejný, In: Š Znam a kol. Pohl'ad do dejín matematiky. SNTL, Bratislava 1986.
- [6] M. Hejný a kol. Teoria vyučovania matematiky 2. SPN, Bratislava 1990.
- [7] M. Hejný, Stehlikova, N. Číselné představy dětí. PedF UK, Praha 1999.
- [8] F. Kuřina, Deset pohledu na geometrii. M a ALBRA, Praha 1996.
- [9] M. Prokopová, Some remarks about pupil's concept of a point. In: 9 th Polish-Czech Mathematical School. Krakow.
- [10] F. Servít, Eukleidovy základy (Elementa). ČJMF, Praha 1907.
- [11] D. J. Struik, Dějiny matematiky. Orbis, Praha 1963.
- [12] P. Vopněka, Rozpravy s geometrií. Panorama, Praha 1989.
- [13] P. Vopěnka, Úhelný kámen evropské vzdělanosti a moci. Práh, Praha 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ec04cc8d-1860-4434-88cb-23bf802f9678