University of Leeds, School of Mathematics
MATH 2051 Geometry of Curves and Surfaces.
Exercises 2: Curvature of Parametrized Curves
Submit on Friday 29 October 2010
1. For each of the following RPCs : R Rn , compute the curvature vector k : R Rn :
(a) (t)
University of Leeds, School of Mathematics
MATH 2051 Geometry of Curves and Surfaces.
Exercises 5: Curvature of Surfaces
Submit on Friday 10 December 2010
1. Show that M : R2 R3 , M (x1 , x2 ) = (x1 , x2 , 1 x2 ) is a regularly parametrized surface. Sketc
University of Leeds, School of Mathematics
MATH 2051 Geometry of Curves and Surfaces.
Exercises 4: Tangent and Normal Spaces
Submit on Friday 26 November 2010
1. Given a point y R3 , nd expressions for the distance from y to (0, 0, 1) and the distance
fro
University of Leeds, School of Mathematics
MATH 2051 Geometry of Curves and Surfaces.
Exercises 1: Regularly Parametrized Curves
Submit on Friday 15 October 2010
1. Determine which of the following are regularly parametrized curves, carefully explaining y
University of Leeds, School of Mathematics
MATH 2051 Geometry of Curves and Surfaces.
Exercises 3: Frenet Frame, Surfaces
Submit on Friday 11 November 2010
1
1. Given that : R R3 has (0) = 2 (1, 1, 0) and (0) = (1, 0, 1) construct [u(0), n(0), b(0)],
the