circumference

Examples of circumference in the following topics:

• Radians

  • The length of the arc around an entire circle is called the circumference of that circle.
  • So the circumference of any circle is $2\pi \approx 6.28$ times the length of the radius.
  • Because the total circumference of a circle equals $2\pi$ times the radius, a full circular rotation is $2\pi$ radians.
  • In fact, radian measure is dimensionless, since it is the quotient of a length (circumference) divided by a length (radius), and the length units cancel.
  • The circumference of a circle is a little more than 6 times the length of the radius.

• Circles as Conic Sections

  • You probably know how to find the area and the circumference of a circle, given its radius.
  • The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654.
  • The length of the circumference, C, is related to the radius, r, and diameter, d, by:
  • As proved by Archimedes, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference, and whose height equals the circle's radius, which comes to π multiplied by the radius squared:

• Introduction to Circles

  • The circumference is the length of the path around the circle.
  • The number $\pi$ is actually defined by this relationship, as the ratio of any circle's circumference to its own diameter.

• Introduction to Variables

  • For example, the relationship between the circumference, $C$, and diameter, $d$, of a circle is described by $\displaystyle \pi =C/d$ .

• Applications of Circles and Ellipses

  • Ellipses are less common, mostly encountered as the orbits of planets, but you should be able to find the area of a circle or an ellipse, or the circumference of a circle, based on information given to you in a problem.