TY - JOUR
T1 - Osculating Circle with Microscopes Within Microscopes
AU - Bair, Jacques
AU - Henry, Valérie
PY - 2013/6/1
Y1 - 2013/6/1
N2 - 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.
AB - 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.
KW - Microscope within microscope
KW - Non-standard analysis
KW - Osculating circle
UR - http://www.scopus.com/inward/record.url?scp=84878364807&partnerID=8YFLogxK
U2 - 10.1007/s10699-012-9320-9
DO - 10.1007/s10699-012-9320-9
M3 - Article
AN - SCOPUS:84878364807
SN - 1572-8471
VL - 18
SP - 319
EP - 325
JO - Fondations of Science
JF - Fondations of Science
IS - 2
ER -