Osculating Circle with Microscopes Within Microscopes

Foundations of Science 18 (2):319-325 (2013)

Abstract
Classically, an osculating circle at a point of a planar curve is introduced technically, often with formula giving its radius and the coordinates of its center. In this note, we propose a new and intuitive definition of this concept: among all the circles which have, on the considered point, the same tangent as the studied curve and thus seem equal to the curve through a microscope, the osculating circle is this that seems equal to the curve through a microscope within microscope
Keywords Osculating circle  Microscope within microscope  Non-standard analysis
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DOI 10.1007/s10699-012-9320-9
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Model-Based Reasoning: Science, Technology, Values.L. Magnani & N. J. Nersessian (eds.) - 2002 - Kluwer Academic/Plenum Publishers.
Epistemic Mediators and Model-Based Discovery in Science.L. Magnani - 2002 - In L. Magnani & N. J. Nersessian (eds.), Model-Based Reasoning: Science, Technology, Values. Kluwer Academic/Plenum Publishers. pp. 305--329.

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