Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.

PREFACE
BIBLIOGRAPHY
CHAPTER 1. CURVES
  1-1 Analytic representation
  1-2 "Arc length, tangent "
  1-3 Osculating plane
  1-4 Curvature
  1-5 Torsion
  1-6 Formulas of Frenet
  1-7 Contact
  1-8 Natural equations
  1-9 Helices
  1-10 General solution of the natural equations
  1-11 Evolutes and involutes
  1-12 Imaginary curves
  1-13 Ovals
  1-14 Monge
CHAPTER 2. ELEMENTARY THEORY OF SURFACES
  2-1 Analytical representation
  2-2 First fundamental form
  2-3 "Normal, tangent plane"
  2-4 Developable surfaces
  2-5 Second fundamental form
  2-6 Euler's theorem
  2-7 Dupin's indicatrix
  2-8 Some surfaces
  2-9 A geometrical interpretation of asymptotic and curvature lines
  2-10 Conjugate directions
  2-11 Triply orthogonal systems of surfaces
CHAPTER 3. THE FUNDAMENTAL EQUATIONS
  3-1 Gauss
  3-2 The equations of Gauss-Weingarten
  3-3 The theorem of Gauss and the equations of Codazzi
  3-4 Curvilinear coordinates in space
  3-5 Some applications of the Gauss and the Codazzi equations
  3-6 The fundamental theorem of surface theory
CHAPTER 4. GEOMETRY ON A SURFACE.
  4-1 Geodesic (tangential) curvature
  4-2 Geodesics
  4-3 Geodesic coordinates
  4-4 Geodesics as extremals of a variational problem
  4-5 Surfaces of constant curvature
  4-6 Rotation surfaces of constant curvature
  4-7 Non-Euclidean geometry
  4-8 The Gauss-Bonnet theorem
CHAPTER 5. SOME SPECIAL SUBJECTS
  5-1 Envelopes
  5-2 Conformal mapping
  5-3 Isometric and geodesic mapping
  5-4 Minimal surfaces
  5-5 Ruled surfaces
  5-6 lmaginaries in surface theory
SOME PROBLEMS AND PROPOSITIONS
APPENDIX: The method of Pfaffians in the theory of curves and surfaces
ANSWERS TO PROBLEMS
INDEX