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.
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Bair, J., Henry, V. Osculating Circle with Microscopes Within Microscopes. Found Sci 18, 319–325 (2013). https://doi.org/10.1007/s10699-012-9320-9
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DOI: https://doi.org/10.1007/s10699-012-9320-9