Lab 1: Local Theory of Plane Curves
Introduction
The most basic objects in differential geometry are plane curves. This first
laboratory examines different ways of presenting plane curves and
their geometric properties. We will be especially concerned with local properties of plane
curves, which can be defined at a point by considering arbitrarily
small neighborhoods of the point. We begin with parametrized plane curves, interpreted as
paths traced out by a moving point. Examples of local properties for
parametrized curves are speed, velocity and
acceleration.
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