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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
License
DOI (Digital Object Identifier)
10.14760/SNAP-2019-013-EN
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snapshots: overview
Mathematical subjects
Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics
Connections to other fields
Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics