Circle As Limiting Case of Other Figures
The circle can be viewed as a limiting case of each of various other figures:
- A Cartesian oval is a set of points such that a weighted sum of the distances from any of its points to two fixed points (foci) is a constant. An ellipse is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
- A superellipse has an equation of the form for positive a, b, and n. A supercircle has b = a. A circle is the special case of a supercircle in which n = 2.
- A Cassini oval is a set of points such that the product of the distances from any of its points to two fixed points is a constant. When the two fixed points coincide, a circle results.
- A curve of constant width is a figure whose width, defined as the perpendicular distance between two distinct parallel lines each intersecting its boundary in a single point, is the same regardless of the direction of those two parallel lines. The circle is the simplest example of this type of figure.
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Famous quotes containing the words circle, limiting, case and/or figures:
“To love someone is to isolate him from the world, wipe out every trace of him, dispossess him of his shadow, drag him into a murderous future. It is to circle around the other like a dead star and absorb him into a black light.”
—Jean Baudrillard (b. 1929)
“I am truly free only when all human beings, men and women, are equally free. The freedom of other men, far from negating or limiting my freedom, is, on the contrary, its necessary premise and confirmation.”
—Mikhail Bakunin (1814–1876)
“The attention of those who frequent the camp-meetings at Eastham is said to be divided between the preaching of the Methodists and the preaching of the billows on the back side of the Cape, for they all stream over here in the course of their stay. I trust that in this case the loudest voice carries it. With what effect may we suppose the ocean to say, “My hearers!” to the multitude on the bank. On that side some John N. Maffit; on this, the Reverend Poluphloisboios Thalassa.”
—Henry David Thoreau (1817–1862)
“She, while her lover pants upon her breast,
Can mark the figures on an Indian chest.”
—Alexander Pope (1688–1744)