Hjelmslev's geometry of reality

Research output: Contribution to journal › Journal article › Research › peer-review

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Hjelmslev's geometry of reality. / Lützen, Jesper.

In: Historia Mathematica, Vol. 54, 2021, p. 95-116.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Lützen, J 2021, 'Hjelmslev's geometry of reality', Historia Mathematica, vol. 54, pp. 95-116. https://doi.org/10.1016/j.hm.2020.08.003

APA

Lützen, J. (2021). Hjelmslev's geometry of reality. Historia Mathematica, 54, 95-116. https://doi.org/10.1016/j.hm.2020.08.003

Vancouver

Lützen J. Hjelmslev's geometry of reality. Historia Mathematica. 2021;54:95-116. https://doi.org/10.1016/j.hm.2020.08.003

Author

Lützen, Jesper. / Hjelmslev's geometry of reality. In: Historia Mathematica. 2021 ; Vol. 54. pp. 95-116.

Bibtex

@article{b3d729e1ce3b444ca48239edc98691e8,
title = "Hjelmslev's geometry of reality",
abstract = "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.",
keywords = "Axiomatization, Descriptive geometry, Didactics, Geometric constructions, Geometry of reality, Johannes Hjelmslev",
author = "Jesper L{\"u}tzen",
year = "2021",
doi = "10.1016/j.hm.2020.08.003",
language = "English",
volume = "54",
pages = "95--116",
journal = "Historia Mathematica",
issn = "0315-0860",
publisher = "Academic Press",

}

RIS

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