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.
Original language | English |
---|---|
Pages (from-to) | 319-325 |
Number of pages | 7 |
Journal | Fondations of Science |
Volume | 18 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2013 |
Keywords
- Microscope within microscope
- Non-standard analysis
- Osculating circle