Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science

2019-11-19

2019

Radis Kostantinos

Ευάγγελος Ράπτης, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Σταύρος Παπασταυρίδης, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Διονύσιος Λάππας, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

ΙΣΟΔΙΑΧΩΡΙΣΙΜΑ ΚΑΙ ΙΣΟΣΥΜΠΛΗΡΩΣΙΜΑ ΣΧΗΜΑΤΑ

Greek

Εquidecomposable and Equicomplementable figures

Beginning my thesis work on shapes, I thought it good to refer, in the first chapter, to the concepts of the area of a shape, the volume of a three dimensional shape as well as to the equidecomposable and the equicomplementable of the shapes. The properties (axioms) definitions and theorems that exist and the structure, in general, are as mentioned in V. G. Boltianskii’s book: Hilbert’s Thirdd Problem (transl. R. A. Silverman) [3]. The second chapter deals with equidecomposable figures in plane and contains the Bolyai-Gerwien theorem. The next chapter contains Hilbert’s 3rd problem. Two different versions of this proof are given which are supported: the first in Dehn-Hadwiger’s theorem [1] and the second in the Bricard treaty [2]. In chapter four there are references to the life and work of F. Hilber, as well as, to his speech at the conference of mathematics in Paris at the turn of the twentieth century. Finally, some teaching extensions are provided for students at all levels of education.

Science

Εquidecomposable , equicomplementable, Hilbert’ third problem

Yes

1

Yes

20

80

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https://pergamos.lib.uoa.gr/uoa/dl/object/2885906