Skip to main content
SpringerLink
Log in

The Rise and Fall of Descriptive Geometry in Denmark

  • Chapter
  • First Online:
Descriptive Geometry, The Spread of a Polytechnic Art

Abstract

The history of descriptive geometry in Denmark is primarily a story of teaching and its institutional setting. Only at the very end did a Danish mathematician contribute original research to the story. The subject was introduced in Denmark around 1830 in connection with the foundation of two new colleges, one civil and one military that were both inspired by the École polytechnique. The subject continued to be taught at the civil polytechnic college for about a century, after which descriptive geometry disappeared from Danish education. At the very end of the period, Hjelmslev’s geometry of reality added an original approach to Danish descriptive geometry; otherwise Danish descriptive geometers limited themselves to importing new ideas from abroad, in particular from France and Germany. However, Danish textbooks and exam questions bear witness to a high theoretical level of the descriptive geometry education in Copenhagen.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    All translations of titles, names, and quotes from Danish are the author’s.

  2. 2.

    For a survey of the many different earlier and later military schools in Denmark, Norway, and Holstein see Rosenløv (1963), in particular the schematic figure p. 185. See also Harnow (2005, pp. 40–42).

  3. 3.

    However, Frédéric Brechenmacher has not been able to find Kellner’s name in the archives of the École polytechnique.

  4. 4.

    Descriptive geometry was taught as a separate course apart from the “mathematics” course.

  5. 5.

    Seidelin also published an elementary textbook in projection drawing (Seidelin 1879) (later eds. 1884, 1895).

  6. 6.

    1873–1950. Originally Hjelmslev was named Petersen, but since the name J. Petersen was already used by his colleague Julius Petersen he changed his last name in 1904.

References

  • Andersen, Kirsti, and Thøger Bang. 1983. Matematik. In Københavns Universitet 1479–1979, ed. Pihl, Mogens, 113–199. Bind XII, Det matematisk-naturvidenskabelige Fakultet, 1. del. København: Gad.

    Google Scholar 

  • Bohr, Harald, and Johannes Mollerup. 1920–1923. Lærebog i Matematisk Analyse, vol. I–IV. København: Jul Gjellerup.

    Google Scholar 

  • Christensen, Dan Charly. 1995. The Ørsted-Ritter Partnership and the Birth of Romantic Natural Philosophy. Annals of Science 52 (2): 153–185.

    Article  MathSciNet  Google Scholar 

  • Eckersberg, Wilhelm Christoffer. 1833. Forsøg til en Veiledning i Anvendelse af Perspektivlæren for unge Malere. Kjøbenhavn: Thieles Bogtrykkeri.

    Google Scholar 

  • ———-. 1841. Linearperspektiven, anvendt paa Malerkunsten. Kjøbenhavn: C.A. Reitzel.

    Google Scholar 

  • Fuchs, Anneli, and Emma Salling (eds.). 2004. Kunstakademiet 1754–2004, Bind III. København: Det Kongelige Akademi for de Skønne Kunster & Arkitekternes Forlag.

    Google Scholar 

  • Goos, Carl (ed.). 1887. Kjøbenhavns Universitet, den polytekniske Læreanstalt og Kommunitetet indeholdende Meddelelser for de akademiske Aar 1864–71 med Sagregister. Kjøbenhavn: Gyldendal.

    Google Scholar 

  • Hansen, Hans Christian. 2002. Fra forstandens slibesten til borgerens værktøj. Regning og matematik i folkets skole 1739–1958. Aalborg: Papers from DCN No. 16.

    Google Scholar 

  • Hansen, Hans Christian et al. 2008. Matematikundervisningen i Danmark i 1900-tallet, vol. 2, 7. ed. Odense: Syddansk Universitetsforlag.

    Google Scholar 

  • Harnow, Henrik. 2005. Den danske Ingeniørs Historie 1850–1920. Herning: Systimes teknologihistorie.

    Google Scholar 

  • Hetsch, Gustav Friedrich, and Georg Frederik Ursin. 1828. Begyndelsesgrunde af den geometriske Tegnelære til Brug for Kunst- og Haandverks-Skoler. Kjöbenhavn: Udgivernes Forlag.

    Google Scholar 

  • Hilbert, David. 1930. Grundlagen der Geometrie, 7. ed. Berlin: Teubner.

    MATH  Google Scholar 

  • Hjelmslev, Johannes. 1904. Deskriptivgeometri. Grundlag for Forelæsninger paa Polyteknisk Læreanstalt. Separate volume of figures. København: Jul. Gjellerup.

    Google Scholar 

  • ———-. 1913. Om grundlaget for den praktiske geometri. Matematisk Tidsskrift A 2: 41–58.

    MATH  Google Scholar 

  • ———-. 1918. Lærebog i Geometri til Brug ved Den Polytekniske Læreanstalt. København: Jul. Gjellerup.

    Google Scholar 

  • ———-. 1923. Die Natürliche Geometrie. Hamburger Mathematische Einzelschriften, 1. Heft.

    Google Scholar 

  • Jessen, Børge. 1939–1941. Lærebog i Geometri. I Afbildninger og analytisk Geometri (1939), II Differentialgeometri (1941). København: Jul. Gjellerup.

    Google Scholar 

  • Kellner, Ludvig Stephan. 1836. Den beskrivende (descriptive) Geometris theoretiske Deel. Figures in separate volume. Kjøbenhavn: Forfatterens Forlag. Second revised ed. 1850.

    Google Scholar 

  • ———-. 1840. Den beskrivende (descriptive) Geometris anvendte Deel. Figures in separate volume. Kjøbenhavn: Forfatterens Forlag. Second revised ed. 1851.

    Google Scholar 

  • Klein, Felix. 1928. Elementarmathematik vom höheren Standpunkte aus Dritte Auflage, Dritter Band: Präzisions- und Approximationsmathematik. 3. ed. Berlin: Springer.

    Book  Google Scholar 

  • Lundbye, Johan Thomas. 1929. Den Polytekniske Læreanstalt 1829–1929. København: Gad.

    Google Scholar 

  • Lützen, Jesper, Gert Sabidussi, and Bjarne Toft. 1992. Julius Petersen 1839–1910. A Biography. Discrete Mathematics 100: 9–82.

    Article  MathSciNet  Google Scholar 

  • Madsen, Tage Gutmann. 2008. Matematikundervisningen ved universiteter og højere læreranstalter. In Fra forstandens slibesten til borgerens værktøj. Regning og matematik i folkets skole 1739–1958, ed. Hansen, Hans Christian, 755–920. Aalborg: Papers from DCN No. 16.

    Google Scholar 

  • Monge, Gaspard. 1827. Géométrie descriptive, 5. ed. Paris: Bachelier.

    Google Scholar 

  • Nielsen, Jørgen Broberg, and Ejvind Slottved. 1983. Fakultetets almindelige historie. In Københavns Universitet 1479–1979, ed. Pihl, Mogens, 1–112. Bind XII, Det matematisk-naturvidenskabelige Fakultet, 1. del. København: Gad.

    Google Scholar 

  • Nielsen, Niels. 1910. Matematikken i Danmark 1801–1908. Bidrag til en Bibliografisk-historisk Oversigt. København, Kristiania: Gyldendal.

    Google Scholar 

  • Petersen, Julius. 1866. Methoder og Theorier til Løsning af Geometriske Konstruktionsopgaver. Kjøbenhavn: Schønberg. second enlarged ed. 1879. Translated 1879 into German and English.

    Google Scholar 

  • Pihl, Mogens (ed.). 1983. Københavns Universitet 1479–1979, Bind XII, Det matematisk-naturvidenskabelige Fakultet, 1. del. København: Gad

    Google Scholar 

  • Rosenløv, Mogens (ed.). 1963. Uddannelsen af Hærens Linieofficerer 1713–1963. Frederiksberg: Hærens Officerskole.

    Google Scholar 

  • Seidelin, Carl Julius Ludvig. 1873. Forelæsninger over deskriptivgeometri. Figures in separate volume. Kjøbenhavn: Forfatterens Forlag. second ed. 1886–87, 3. ed. 1895–96.

    Google Scholar 

  • ———-. 1879. Elementær Lære i Projektionstegning. Kjøbenhavn: Hauberg. 2. ed. 1884, 3. ed. 1895.

    Google Scholar 

  • Steen, Adolph. 1879. Polyteknisk Læreanstalts første halvhundrede Aar 1829–1879. Kjøbenhavn: Bianco Luno.

    Google Scholar 

  • Tychsen, Valentin Emil, Hieronymus Georg Zeuthen, and Poul Heegaard. 1937. Kellner, Ludvig Stephan. In Dansk Biografisk Leksikon, vol. XII, 390–391. København: Schultz.

    Google Scholar 

  • Wagner, Michael F. 1998. Det Polytekniske Gennembrud. Århus: Aarhus Universitetsforlag.

    Google Scholar 

  • Zeuthen, Hieronymus Georg. 1887–1905. Ursin, Georg Frederik Krüger. In Dansk Biografisk Lexikon, ed. Carl Frederik Bricka, vol. 18. Kjøbenhavn: Gyldendal.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Jesper Lützen

Authors
  1. Jesper Lützen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jesper Lützen .

Editor information

Editors and Affiliations

  1. UFR Sciences et Techniques, Nantes, France

    Évelyne Barbin

  2. Department of Mathematics, Sapienza–University of Rome, Rome, Italy

    Marta Menghini

  3. University of Wuppertal, Wuppertal, Germany

    Klaus Volkert

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lützen, J. (2019). The Rise and Fall of Descriptive Geometry in Denmark. In: Barbin, É., Menghini, M., Volkert, K. (eds) Descriptive Geometry, The Spread of a Polytechnic Art. International Studies in the History of Mathematics and its Teaching. Springer, Cham. https://doi.org/10.1007/978-3-030-14808-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-14808-9_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14807-2

  • Online ISBN: 978-3-030-14808-9

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation