ABSTRACT

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditi

chapter 1|4 pages

Definition of a Curve

chapter 3|4 pages

The Regular Curve and its Representations

chapter 4|4 pages

Straight Line Tangent to a Curve

chapter 5|4 pages

Osculating Plane of a Curve

chapter 6|6 pages

The Arc Length of a Curve

chapter 7|10 pages

The Curvature and Torsion of a Curve

chapter 8|4 pages

Osculating Circle of a Plane Curve

chapter 9|8 pages

Singular Points of Plane Curves

chapter 10|2 pages

Peano's Curve

chapter 11|2 pages

Envelope of the Family of Curves

chapter 12|6 pages

Frenet Formulas

chapter 16|4 pages

Osculating Sphere

chapter 17|10 pages

Special Planar Curves

chapter 18|6 pages

Curves in Mechanics

chapter 19|2 pages

Curve Filling a Surface

chapter 20|6 pages

Curves with Locally Convex Projection

chapter 21|4 pages

Integral Inequalities for Closed Curves

chapter 23|12 pages

Conditions for a Curve to be Closed

chapter 24|4 pages

Isoperimetric Property of a Circle

chapter 25|2 pages

One Inequality for a Closed Curve

chapter 27|8 pages

Delaunay's Problem

chapter 28|6 pages

Jordan's Theorem on Closed Plane Curves

chapter 29|10 pages

Gauss's Integral for Two Linked Curves

chapter 30|8 pages

Knots

chapter 31|12 pages

Alexander's Polynomial

chapter 32|8 pages

Curves in n-dimensional Euclidean Space

chapter 34|4 pages

Generalization of the Fenchel Inequality

chapter 35|4 pages

Knots and Links in Biology and One Mystery