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)
“O wily painter, limiting the scene
From a cacophony of dusty forms
To the one convulsion,”
—Thom Gunn (b. 1929)
“Sculpture and painting are very justly called liberal arts; a lively and strong imagination, together with a just observation, being absolutely necessary to excel in either; which, in my opinion, is by no means the case of music, though called a liberal art, and now in Italy placed even above the other two—a proof of the decline of that country.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“But that wasn’t fancy enough for Lord Byron, oh dear me no, he had to invent a lot of figures of speech and then interpolate them,
With the result that whenever you mention Old Testament soldiers to
people they say Oh yes, they’re the ones that a lot of wolves dressed up in gold and purple ate them.”
—Ogden Nash (1902–1971)