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Touching the transcendentals: tractional motion from the birth of calculus to future perspectives

Instantanés de recherche mathématique à Oberwolfach

Touching the transcendentals: tractional motion from the birth of calculus to future perspectives

When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus. We reinterpret “tractional motion”, a late 17th century method to draw transcendental curves, in order to reintroduce “ideal machines” in math foundation for a constructive approach to calculus that avoids the concept of infinity.

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Sujet mathématique

Algèbre et théorie des nombres
Analyse
Géométrie et Topologie

Liens avec d'autres domaines

Informatique
Pensées mathématiques

Auteur(s)

Pietro Milici

Licence

DOI

10.14760/SNAP-2019-013-EN

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snapshots-2019-013.pdf

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      Sujet mathématique

      Algèbre et théorie des nombres
      Analyse
      Pédagogie et éducation
      Mathématiques discrètes et fondements des mathématiques
      Géométrie et Topologie
      Calcul numérique et calcul scientifique
      Théorie des probabilités et statistique

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      Physique
      Pensées mathématiques

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