Thesis (Selection of subject)Thesis (Selection of subject)(version: 341)
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Porovnání axiomatických systémů geometrie u Euklida a Hilberta z hlediska didaktiky matematiky
Thesis title in Czech: Porovnání axiomatických systémů geometrie u Euklida a Hilberta z hlediska didaktiky matematiky
Thesis title in English: Comparison of Euclid's and Hilbert's Axiomatic Systems of Geometry from the Didactic Viewpoint
Key words: Euklides, Hilbert, axiomatická metóda
English key words: Euclid, Hilbert, axiomatic method
Academic year of topic announcement: 2014/2015
Type of assignment: Bachelor's thesis
Thesis language: čeština
Department: Katedra matematiky a didaktiky matematiky (41-KMDM)
Supervisor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Author: hidden - assigned by the advisor
Date of registration: 26.11.2014
Date of assignment: 26.11.2014
Date and time of defence: 19.05.2016 09:00
Venue of defence: M. Rettigové 4, Praha 1, R318, 318, matematika, 3. patro, vlevo
Date of electronic submission:15.04.2016
Date of proceeded defence: 19.05.2016
Course: Diploma Thesis (OSZD004)
Reviewers: Mgr. Marie Holíková, Ph.D.
 
 
 
Guidelines
Student porovná axiomatické budování geometrie u Euklida a Hilberta z pohledu didaktiky matematiky.
References
Heath, T.: The thirteen books of Euclid's Elements
Dedekind, R.: Stetigkeit und irrazionale Zahlen
Hilbert, D.: Grundlagen der Geometrie
Hadamard, J.: Lessons in Geometry.
Preliminary scope of work
Student se obeznámí s kritikou Euklidových Základů z moderního hlediska (spojitost, uspořádání, ...)
Provede analýzu základních mezer v Euklidově axiomatice jak jsou diskutovány v literatuře.
Porovná "chybné" důkazy u Euklida s moderníma důkazy u Hilberta a Hadamarda.
Preliminary scope of work in English
The student will study the criticisms of Euclid's Elements from the modern viewpoint axioms of continuity, axioms of order, ...)
He will analyze the basic gaps in the Euclidean system of axioms which were discussed in the literature.
He will compare the "false proofs" given by Euclid, with the modern ones given by Hilbert and Hadamard.
 
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