Mathematical Induction in Ancient Greek Mathematics

Postgraduate Thesis uoadl:1325739 734 Read counter

Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
2016-12-03
Year:
2016
Author:
Κιούφτη Ροϊδούλα
Supervisors info:
Στυλιανός Νεγρεπόντης Ομότιμος Καθηγητής Τμημ. Μαθηματικών ΕΚΠΑ, Β. Φαρμάκη Καθηγήτρια ΕΚΠΑ, , Γ. Ψυχάρη Επικ. Καθηγητής ΕΚΠΑ
Original Title:
Η Μαθηματική Επαγωγή στα Αρχαία Ελληνικά Μαθηματικά
Languages:
Greek
Translated title:
Mathematical Induction in Ancient Greek Mathematics
Summary:
The purpose of the present Master’s Thesis on Mathematical Induction in Ancient Greek Mathematics is twofold,
(a) to record and evaluate the position of scholars, especially Freudenthal (1953), Mueller (1981), Unguru (1991), Fowler (1994), Acerbi (2000), on the question of presence and exact form of the deductive method of complete mathematical induction in Greek Mathematics, and
(b) to present, in an initial and preliminary form, our position on the subject, a position that is differentiated from the existing ones.
Our research takes into account the ancient sources, including Euclid’s Elements, the presentation of the side and diameter numbers by Plato, Theon, Iamblichus, Proclus, the second hypothesis of the Platonic dialogue Parmenides, Archimedes’ work On Spirals, Nicomachus’ Introduction to Arithmetic, the propositions on ‘Arbelos’ in Pappus’ Collection.
We also study the basic medieval sources related to mathematical induction, including the Arabs Abu- Kamil, Al-Karaji, Al-Samaw’al and Ibn al-Haytham, the French-Jewish Levi Ben Gerson, and Francisco Maurolico, of Greek origin.
The reason we delve with the medieval period lies with our intent to separate, as far as this is possible, the instances of inductive reasoning of that period that in essence constitute continuation of techniques already occurring in Greek Mathematics from those that may be genuine steps beyond Greek methods.
Main subject category:
Science
Other subject categories:
Mathematics
Keywords:
ancient Greek Mathematics, mathematical induction, Euclid’s Elements, Platonic dialogue Parmenides, side and diameter numbers, Archimedes, ‘Arbelos’.
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
44
Number of pages:
144
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