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The perimeter of a circle is called a special
name other than perimeter: circumference. The circumference of a circle is
the length of the curve that encloses that circle.
A circle is defined by only two things: its center
and its radius. Two circles with the same center
and the same radius are the same circle. Therefore, the circumference of a
circle must depend on one of these, or both. In fact, the circumference is
dependent solely on the radius of a circle: circumference equals 2Πr, where r
denotes the length of the radius. Another way to state the formula is Πd,
where d denotes the length of the diameter of the
circle, which is, of course, twice that of the radius. A clever way to remember
the formula for circumference is with the sentence "See two pies run." This
sentence corresponds to written version of the formula, C = 2Πr.

Another way to think of the curve that encloses a circle is through the 360
degree arc of that
curve. Thus, the circumference of a circle is the length of the 360 degree arc
of that circle. Since we know that the circumference of a 360 degree arc is
2Πr, where r is the length of the radius, we can calculate the length of
various arcs of a circle, provided that we know the radius of such a circle.
For example, the length of a 180 degree arc must be half the circumference of
the circle, the product of pi and the radius. The length of any arc is equal to
whatever fraction of a full rotation the arc spans multiplied by the
circumference of the circle. A 45 degree arc, for example, spans one-eighth of
a full rotation, and is therefore equal to one-eighth the circumference of that
circle. The length of an arc of n degrees equals (n/360) times the
circumference. Below these concepts are pictured.