Mathematical model (object)

mathematical model is a model of a geometric form , most often made for a pedagogical approach.

Characteristics

Mathematical models are mainly made during the xix th century educational purposes, to help visualize mathematical surfaces (mainly cubic and quadric ) 3 . The models reproduce in space shapes that can be difficult to grasp on paper or on a simple blackboard and allow to illustrate their properties concretely 4 , 5 . The methods of realization vary: sculptures in plasteror in wood, surfaces materialized by tensioned wires (especially for the regulated surfaces ), etc.

In the xx th century, the approach to changes in the research and teaching of geometry quickly render obsolete the production of these mathematical models. Their use is forgotten from the 1920s 4 .

Collections

At the end of the xix th century and beginning of the xx th century, several universities have true collections of mathematical models 6 . Some have kept these collections, among which 7 :

  • Dresden Technical University ( Dresden ): about 400 models 8
  • University of Göttingen ( Göttingen ) 9
  • University of Groningen ( Groningen ) 10
  • Institut Henri-Poincaré ( Paris ): about 500 models, a hundred permanently exhibited in the library of the institute 4
  • Tokyo University ( Tokyo ) 11
  • University of Arizona ( Tucson ) 12
  • University of Turin ( Turin ): about 180 models 13
  • Smithsonian Institution ( Washington ).

Art

If the models are neglected in the mathematical context, they are rediscovered by two art movements in the 1930s, the constructivist and surrealist 14 .

The abstract sculptor Barbara Hepworth , evolving in the constructivist movement, seems to be inspired by mathematical models in several of her works. Russian artist Naum Gabo studies mathematical models during her stay in Paris. His son-based constructions seem to be inspired by them, as well as the influence of Hepworth.

In the surrealist movement, Man Ray made between 1934 and 1936 a photographic series of models from the Institut Henri Poincaré ; he then made a series of paintings staging them, entitled Shakespearian Equations 4 . André Breton cites mathematical models in the magazine Cahiers d’art in 1936 15 .

Annexes

On other Wikimedia projects:

  • Mathematical Models , on Wikimedia Commons

References

  1. ↑ ( de ) ” Modell einer Minimalfläche mit einer Lemniskate als Geodätischer Linie ”  [ archive ] , Universitätssammlungen in Deutschland
  2. ↑ ( de ) ” Modell der Raumkurve 4. Ordnung erster Art und ihre abwickelbaren Flächen [Schilling XII, 1/159] ”  [ archive ] , Universitätssammlungen in Deutschland
  3. ↑ ( in ) Angela Vierling-Claassen, ” Collections of Mathematical Models ”  [ archive ]
  4. ↑ a , b , c and d Mathematical models ”  [ archive ] , Institut Henri-Poincaré
  5. ↑ Isabelle Fortuné, ” Man Ray and mathematical objects ” Photographic Studies , o 6, ( read online  [ archive ] )
  6. ↑ ( in ) Daina Tamina ” Mathematicians in Paris – IV (mathematical models) ”  [ archive ] , Hyperbolic Crochet,
  7. ↑ ( in ) Angela Vierling-Claassen, ” Schools and Museums with Models ”  [ archive ]
  8. ↑ ( de ) ” Mathematishe Modelle ”  [ archive ] , Technical University of Dresden
  9. ↑ ( de ) ” Göttinger Mathematical Sammlung Modelle und Instrumente ”  [ archive ] , University of Göttingen
  10. ↑ ( in ) ” Mathematical models of surfaces ”  [ archive ] , University of Groningen
  11. ↑ ( ja ) ” 数 理 科学研究 科 所 蔵 蔵 蔵 幾何学 幾何学 模型 ”  [ archive ] , University of Tokyo
  12. ↑ ( in ) ” Mathematical Teaching Tools in the Department of Mathematics ”  [ archive ] , University of Arizona
  13. ↑ ( it ) ” Raccolte Museali Italiane di Modelli for the Studio delle Matematiche Superiori [ archive ] , University of Turin
  14. ↑ ( of ) Angela Vierling-Claassen, ” Mathematical Models and Modern Art ”  [ archive ]
  15. ↑ André Breton, ” Crisis of the object ,” Cahiers d’Art , o 1-2,p.  21-26

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