Maple exercises for Differential Geometry: A Geometric Introduction

The files are available in three formats:

  1. The files ending .html are copies of what is in the Appendix C of the book.
  2. The files ending in .mws were written on a Mac running Maple V Release 4 and exported as "Raw Data". In theory, you should be able to download these and get worksheets that will run on whatever platform you are using.
  3. The files ending in .txt were exported as Maple Text files. Hopefully they will transfer easily to whatever platform you are using.
Several of these programs call the file diffgeo_defs, a text file that contains many standard functions . The lines that call this file are of course Cornell-specific, and you will want to insert the appropriate pathname for your machine.

If you have questions/comments/suggestions, I would love to hear them.

Have fun!

David Henderson

dwh2@cornell.edu

Standard Functions -- diffgeo_defs

Computer Exercise 1.6: Strake -- strake.mws or .txt

Computer Exercise 1.7: Surfaces of Revolution -- surface_of_revolution.mws or .txt

Computer Exercise 1.9: Surfaces as Graph of a Function -- Monge_patch.mws or .txt

Computer Exercise 2.2: Tangent Vectors to Curves -- tangents.mws or .txt

Computer Exercise 2.3: Curvature and Tangent Vectors -- curvature_vectors.mws or .txt

Computer Exercise 2.4a: Osculating Planes -- osculating_plane.mws or .txt

Computer Exercise 2.4b: Osculating Circles -- osculating_circle.mws or .txt

Computer Exercise 2.6: Frenét Frame -- frenet_frame.mws or .txt

Computer Exercise 3.1: Tangent Planes to Surfaces

Computer Exercise 3.2a: Curves on a Surface -- domain_curve_and_surface.mws or .txt

Computer Exercise 3.2b: Extrinsic Curvature Vectors -- curve_on_surface_extrinsic.mws or .txt

Computer Exercise 3.3: The Three Curvature Vectors -- normal_and_geodesic_curvature.mws or .txt

Computer Exercise 3.4: Ruled Surfaces -- ruled_surfaces.mws or .txt

Computer Exercise 5.2: Non-dissectable Polyhedron -- polyhedron.mws or .txt

Computer Exercise 5.5: Sign of (Gaussian) Curvature -- Gaussian_Curvature.mws or .txt

Computer Exercise 6.1: Multiple Principle Directions -- problem_6.1.mws or .txt

Computer Exercise 6.3: Gauss Map -- Gauss_Map.mws or .txt

Computer Exercise 6.6: Helicoid to Catenoid -- helicoid_catenoid.mws or .txt