circumference

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.