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MAA Reviews

Dirk J. Struik

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