Osculating Circle with Microscopes Within Microscopes

Jacques Bair, Valérie Henry

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    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 languageEnglish
    Pages (from-to)319-325
    Number of pages7
    JournalFondations of Science
    Issue number2
    Publication statusPublished - 1 Jun 2013


    • Microscope within microscope
    • Non-standard analysis
    • Osculating circle


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