Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 11 (2019) no. 1, pp. 5-24
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Baldwin, John T.; Mueller, Andreas. Autonomy of Geometry. Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 11 (2019) no. 1, pp. 5-24. http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a0/
@article{AUPCDM_2019_11_1_a0,
author = {Baldwin, John T. and Mueller, Andreas},
title = {Autonomy of {Geometry}},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia},
pages = {5--24},
year = {2019},
volume = {11},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a0/}
}
TY - JOUR
AU - Baldwin, John T.
AU - Mueller, Andreas
TI - Autonomy of Geometry
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
PY - 2019
SP - 5
EP - 24
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a0/
LA - en
ID - AUPCDM_2019_11_1_a0
ER -
%0 Journal Article
%A Baldwin, John T.
%A Mueller, Andreas
%T Autonomy of Geometry
%J Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
%D 2019
%P 5-24
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a0/
%G en
%F AUPCDM_2019_11_1_a0
In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.
