circumference

Algebra

(noun)

The length of a line that bounds a circle.

Related Terms

  • radian
  • arc
Physics

(noun)

The line that bounds a circle or other two-dimensional figure

Examples of circumference in the following topics:

  • Eratosthenes' Experiment

    • Using basic geometry, Greek mathematician Eratosthenes determined the circumference of the Earth within 0.4% error of today's value.
    • Eratosthanes sought to know the circumference of Earth.
    • To measure its circumference, he devised a method that used the rays of sunlight that hit Earth which he assumed arrive parallel.
    • But the circumference of a sphere equals π times its diameter:
    • Thus his measurement of the Earth circumference (some 2000 years ago) was in error: Less than actual by only one-tenth of a percent.
  • 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:
  • Angular Position, Theta

    • We know that for one complete revolution, the arc length is the circumference of a circle of radius r.
    • The circumference of a circle is 2πr.
    • The arc length Δs is described on the circumference.
  • Introduction to Circles

    • The circumference is the length of the path around the circle.
    • It is the ratio of any circle's circumference to its own diameter.
  • Wave Nature of Matter Causes Quantization

    • Assuming that an integral multiple of the electron's wavelength equals the circumference of the orbit, we have:
    • The third and fourth allowed circular orbits have three and four wavelengths, respectively, in their circumferences.
  • de Broglie and the Bohr Model

    • By assuming that the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit, we have the equation:
    • (c) If the wavelength does not fit into the circumference, the electron interferes destructively; it cannot exist in such an orbit.
  • Inference for linear regression

    • Is the gestational age (time between conception and birth) of a low birth-weight baby useful in predicting head circumference at birth?
    • Twenty-five low birth-weight babies were studied at a Harvard teaching hospital; the investigators calculated the regression of head circumference (measured in centimeters) against gestational age (measured in weeks).
    • (a) What is the predicted head circumference for a baby whose gestational age is 28 weeks?
    • Does the model provide strong evidence that gestational age is significantly associated with head circumference?
    • There is an association between gestational age and head circumference.
  • Kinematics of UCM

    • The arc length $\Delta s$ is described on the circumference.
  • Using Interference to Read CDs and DVDs

    • This is because the center tracks are smaller in circumference and therefore can be read quicker.
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