Examples of symmetry in the following topics:
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- 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.
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- When domain has a cylindrical symmetry and the function has several specific characteristics, apply the transformation to polar coordinates.
- In R2, 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.
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- 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 R3 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 R3 have spherical symmetry.
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- 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.
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- 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.
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- 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):
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- The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis .