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

Snapshots of modern mathematics from 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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Mathematical subjects

Algebra and Number Theory
Analysis
Geometry and Topology

Connections to other fields

Computer Science
Reflections on Mathematics

Author(s)

Pietro Milici

License

DOI (Digital Object Identifier)

10.14760/SNAP-2019-013-EN

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snapshots-2019-013.pdf

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