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:
“Perchance we may,
Where now this night is day,
And even through faith of still averted feet,
Making full circle of our banishment,
Amazed meet;”
—Coventry Kersey Dighton Patmore (1823–1896)
“O wily painter, limiting the scene
From a cacophony of dusty forms
To the one convulsion,”
—Thom Gunn (b. 1929)
“True and false are attributes of speech not of things. And where speech is not, there is neither truth nor falsehood. Error there may be, as when we expect that which shall not be; or suspect what has not been: but in neither case can a man be charged with untruth.”
—Thomas Hobbes (1588–1679)
“It could probably be shown by facts and figures that there is no distinctly native American criminal class except Congress.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)