Fall 1998:


Chapter. I

18 September 1998
  • You are expected to solve all exercises at the end of each sections of Manfredo do Carmo. The following problems are from the Eisenharts book.
  • The binormal at a point M of a curve is the limiting position of the common perpendicular to tangents at M and M' , as M' approaches M.
  • Find a necessary and sufificient condition that a curve lie upon a sphere.
  • Find the intrinsic and paramteric equations of a plane curve which is such that the segment on any tangent between the point of contact and the projection of a fixed point is of constant length.
  • Find the intrinsic equation of the plane curve which meets under the constant angle all the lines passing through a fixed point.
  • Investigate the curve which is the locus of the point on the principal normal of a given curve and at constant distance from the later.
  • Find the vector representing the rate of change of the acceleration of a moving point.

    Last update September 1998