Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Pitsas Kwnstantinos
Supervisors info:
Δ. Λάππας Αναπλ. Καθηγητής Τμημ. Μαθηματικών ΕΚΠΑ
Original Title:
Mε Αφορμή το θεώρημα του Μorley: Το σχήμα στο νομοποιητικό πλαίσιο της Ευκλείδειας Γεωμετρίας.
Translated title:
On the occasion of Morley theorem: The validation of figure within the frame of Euclidean geometry.
Summary:
MORLEY’s MIRACLE
The points of intersection of adjacent trisectors of any triangle form an equilateral triangle.
Morley’s theorem was discovered around 1899 and became known in 1924. It has since attracted the attention of the mathematics community as being extraordinary given that there is no structural proof.
In our dissertation:
1. We study the concept of scheme as well as its validation within the frame of an axiomatic theory, in accordance with the aforesaid theorem.
2. We historically follow several methods of proof of the result, from the “geometric” to the fully algebrized, e.g. Alain Connes proof.
3. We research on the generalizations or/and the expansion of the theorem in the frame of the Euclidean Geometry as well as with the use of IT, aiming to disengage the scheme from teacher supervision, in the context of teaching in Upper Secondary School students.
Main subject category:
Science
Other subject categories:
Mathematics
Keywords:
conjecture, proof, proving argument, Morley, geometric shape, teaching geometry.
