symmetry

(noun)

Exact correspondence on either side of a dividing line, plane, center or axis.

Related Terms

  • asymptote

Examples of symmetry in the following topics:

  • Cylindrical and Spherical Coordinates

    • Cylindrical and spherical coordinates are useful when describing objects or phenomena with specific symmetries.
    • While Cartesian coordinates have many applications, cylindrical and spherical coordinates are useful when describing objects or phenomena with specific symmetries.
    • Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with a round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, and so on.
    • Spherical coordinates are useful in connection with objects and phenomena that have spherical symmetry, such as an electric charge located at the origin.
  • Double Integrals in Polar Coordinates

    • When domain has a cylindrical symmetry and the function has several specific characteristics, apply the transformation to polar coordinates.
    • In $R^2$, if the domain has a cylindrical symmetry and the function has several particular characteristics, you can apply the transformation to polar coordinates, which means that the generic points $P(x, y)$ in Cartesian coordinates switch to their respective points in polar coordinates.
    • This is the case because the function has a cylindrical symmetry.
    • In general, the best practice is to use the coordinates that match the built-in symmetry of the function.
  • Triple Integrals in Spherical Coordinates

    • When the function to be integrated has a spherical symmetry, change the variables into spherical coordinates and then perform integration.
    • When the function to be integrated has a spherical symmetry, it is sensible to change the variables into spherical coordinates and then perform integration.
    • In $R^3$ some domains have a spherical symmetry, so it's possible to specify the coordinates of every point of the integration region by two angles and one distance.
    • Spherical coordinates are useful when domains in $R^3$ have spherical symmetry.
  • Curve Sketching

    • Determine the symmetry of the curve.
    • If the exponent of $x$ is always even in the equation of the curve, then the $y$-axis is an axis of symmetry for the curve.
    • Similarly, if the exponent of $y$ is always even in the equation of the curve, then the $x$-axis is an axis of symmetry for the curve.
  • Triple Integrals in Cylindrical Coordinates

    • When the function to be integrated has a cylindrical symmetry, it is sensible to integrate using cylindrical coordinates.
    • When the function to be integrated has a cylindrical symmetry, it is sensible to change the variables into cylindrical coordinates and then perform integration.
  • Applications to Economics and Biology

    • Since we can assume that there is a cylindrical symmetry in the blood vessel, we first consider the volume of blood passing through a ring with inner radius $r$ and outer radius $r+dr$ per unit time ($dF$):
  • Linear and Quadratic Functions

    • The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis .
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.