Quadrisecants give new lower bounds for the ropelength of a knot.
Rational approximation of rotation minimizing frames using Pythagorean-hodograph cubics.
Recursion in curve geometry.
Reflections on spheres and cylinders of revolution.
Regular homotopy and total curvature I: Circle immersions into surfaces.
Relations entre les rayons de courbure de quelques systèmes de courbes
Relaxed hyperelastic curves
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.
Remarks on the symmetries of planar fronts.
A front is the projection on the plane of a Legendrian immersion of a circle in the space of the contact elements of that plane. I analyze the symmetries of a generic front with respect to the group generated by the involutions reversing the orientation of the plane, the orientation of the preimage circle and the coorientation of the contact plane.
Remarque sur une equation differentielle du premier ordre
Remarques sur une classe générale de surfaces, et en particulier sur la surface lieu des points dont la somme des distances à deux droites fixes est constante
Rotation indices related to Poncelet’s closure theorem
Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.
Sätze vom Holditch-Typ für ebene Kurven.
Schallfronten an ebenen Kurven. I.
Schallfronten an ebenen Kurven. III. (Sonic wave fronts at plane curves. III).
Self-parallel curves.
Solution de la question d'analyse proposée au concours d'agrégation de 1875
Solution de la question de mathématiques spéciales, proposée au concours d'admission à l'École polytechnique (1875)
Solving ordinary differential equation systems by approximation in a graphical way.
Some characterizations of special curves in the Euclidean space .
Some Global Properties of Plane Curves