Circle: Difference between revisions
(Created page with "A '''circle''' is a closed curve on a plane, which is equidistant from a point. A circle should be distinguished from the closely related concept of a loop, or an <math>S^1</math>. To emphasize the distinction from loops, a circle is sometimes called a '''rigid circle'''. Circles are one of the central concepts objects of classical geometry. == Examples == === Circles === === Non-circles ===") |
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=== Circles === | === Circles === | ||
[[File:Circle.png|thumb|Figure 1: A circle. ]] | |||
An example of circle can be seen in figure (1). | |||
=== Non-circles === | === Non-circles === | ||
The letter Ω is not a circle, because it is not a closed curve. | |||
== The traditional concept == | |||
In standard mathematics, a circle means a ''perfect'' circle. A perfect circle is like a circle, except that it is supposed to lie in a perfectly flat and infinitely thin plane, the curve of the circle is supposed to have no width, and distance from the circle to its center is supposed to be perfectly uniform. | |||
Although standard mathematicians commonly describe things like figure (1) as circles (because it's ''practical''!!), if they are being careful then they will say figure (1) is technically not a circle, but rather an imperfect representation of a circle. It is imperfect because it has nonzero thickness, and because its distance from its center is not uniform. By contrast, Objective Mathematics says that figure (1) literally ''is'' a circle.<ref group="note">Whether or not figure (1) is deemed a circle depends on context. In our present context, where we are considering sketches of math concepts, we may identify it as a circle. If the context was that we were designing a precision scientific instrument, we probably wouldn't identify it as a circle. </ref> | |||
Revision as of 23:50, 20 January 2024
A circle is a closed curve on a plane, which is equidistant from a point. A circle should be distinguished from the closely related concept of a loop, or an . To emphasize the distinction from loops, a circle is sometimes called a rigid circle.
Circles are one of the central concepts objects of classical geometry.
Examples
Circles
An example of circle can be seen in figure (1).
Non-circles
The letter Ω is not a circle, because it is not a closed curve.
The traditional concept
In standard mathematics, a circle means a perfect circle. A perfect circle is like a circle, except that it is supposed to lie in a perfectly flat and infinitely thin plane, the curve of the circle is supposed to have no width, and distance from the circle to its center is supposed to be perfectly uniform.
Although standard mathematicians commonly describe things like figure (1) as circles (because it's practical!!), if they are being careful then they will say figure (1) is technically not a circle, but rather an imperfect representation of a circle. It is imperfect because it has nonzero thickness, and because its distance from its center is not uniform. By contrast, Objective Mathematics says that figure (1) literally is a circle.[note 1]
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