[Turkmath:483] Gebze Technical University, Department of Mathematics Colloquium

[Tülay Yıldırım]

Sayin Liste Uyeleri,

GTU Matematik Bölümü Genel Seminerleri kapsamında,
08 Mayıs Cuma günü saat 15:00'da David PİERCE
(Mimar Sinan Güzel Sanatlar Universitesi) Moleküler Biyoloji
ve Genetik Bölümü konferans salonunda bir seminer
verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.

Saygılarımızla,

Title: The Sense of Proportion in Euclid

Abstract: A proportion is an identification of ratios.  In the Elements, Euclid
(c. 300 b.c.e.) gives two definitions of a proportion: a clear
definition for arbitrary magnitudes, and an unclear definition for
numbers.  A positive real number, as defined by Richard Dedekind
(1831--1916), can be understood as a ratio of magnitudes in Euclid's
sense.  However, unlike Euclid, Dedekind establishes the *existence*
of all of the so-called real numbers: this has been overlooked, at
least by some of Dedekind's contemporaries.  It has also been thought
that Euclid's ratios of numbers are just fractions in the modern
sense; but this makes Euclid wrong in ways that he is not likely to
be wrong.  Euclid is *more* careful than we often are today
with the foundations of number theory.  He proves rigorously that in
an ordered ring whose positive elements are well-ordered,
multiplication is commutative.  Seeing this can be helped by treating
the reading of Euclid as an instance of doing history: history in the
sense worked out by the philosopher and historian R. G. Collingwood
(1889--1943) in several of his book



Dear all,

There will be a seminar in Gebze Technical University (GTU) on 8th of
May by David PİERCE (MSGSU)
Time  and  place:  At 15:00 in Department of Molecular Biology and,
Genetic, Building C, Auditorium.
Title: The Sense of Proportion in Euclid

Abstract: A proportion is an identification of ratios.  In the Elements, Euclid
(c. 300 b.c.e.) gives two definitions of a proportion: a clear
definition for arbitrary magnitudes, and an unclear definition for
numbers.  A positive real number, as defined by Richard Dedekind
(1831--1916), can be understood as a ratio of magnitudes in Euclid's
sense.  However, unlike Euclid, Dedekind establishes the *existence*
of all of the so-called real numbers: this has been overlooked, at
least by some of Dedekind's contemporaries.  It has also been thought
that Euclid's ratios of numbers are just fractions in the modern
sense; but this makes Euclid wrong in ways that he is not likely to
be wrong.  Euclid is *more* careful than we often are today
with the foundations of number theory.  He proves rigorously that in
an ordered ring whose positive elements are well-ordered,
multiplication is commutative.  Seeing this can be helped by treating
the reading of Euclid as an instance of doing history: history in the
sense worked out by the philosopher and historian R. G. Collingwood
(1889--1943) in several of his book

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