Hjelmslev's geometry of reality
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Hjelmslev's geometry of reality. / Lützen, Jesper.
I: Historia Mathematica, Bind 54, 2021, s. 95-116.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Hjelmslev's geometry of reality
AU - Lützen, Jesper
PY - 2021
Y1 - 2021
N2 - During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.
AB - During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.
KW - Axiomatization
KW - Descriptive geometry
KW - Didactics
KW - Geometric constructions
KW - Geometry of reality
KW - Johannes Hjelmslev
U2 - 10.1016/j.hm.2020.08.003
DO - 10.1016/j.hm.2020.08.003
M3 - Journal article
AN - SCOPUS:85094149265
VL - 54
SP - 95
EP - 116
JO - Historia Mathematica
JF - Historia Mathematica
SN - 0315-0860
ER -
ID: 257869678