Curves,
r] lengths,
Curves, lengths, and curvatures
7.1 Curves and lengths One of the main purposes of this chapter
may seem at first sight to be quite modest. We want to show that the
length L of the circular arc of Figure 7.11, in which dBCD
is a rectangle and the arc is tangent to CD at D, satisfies
the inequality
(7.12) F,1B1 5 L < i C! + (DI.
Before we ask our little sister to solve the problem, we
A' 'D should ask ourselves a question that shows us that the
Figure 7.11 problem is not completely simple. What is a circular arc,
and how do we know that it determines a number that can
be called its length? It is clear that we need some definitions before we
can do anything.
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