A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion
- Autori: milici, p
- Anno di pubblicazione: 2014
- Tipologia: Capitolo o Saggio (Capitolo o saggio)
- OA Link: http://hdl.handle.net/10447/105087
Abstract
Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geometrical and finitistic axiomatic foundation (like Euclid’s planar geometry) for a class of differential problems. In particular, after a brief historical introduction, a model of such machines (i.e., the suggested components) is presented. Then, we introduce some preliminary results about generable functions, an example of a “tractional” planar machine embodying the complex exponential function, and, finally, a didactic proposal for this kind of artifact.