Concept
Circle
Overview
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc.
The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Circle is discussed.
This circle thus appearing is called the [Greek omitted] or halo; and there is constantly such a circle seen by us, when such a density of sight happens. Having taken a survey of the general parts of the world, I will take a view of the particular members of it.
Plutarch, Complete Works of Plutarch — Volume 3
names the idea; states what it is; opens on it
Wherefore since the breadth of the Spectrum PT is not increased by the Refraction sideways, it is certain that the Rays are not split or dilated, or otherways irregularly scatter'd by that Refraction, but that every Circle is by a regular and uniform Refraction translated entire into another Place, as the Circle AG by the greatest Refraction into the place _ag_, the Circle BH by a less Refraction into the place…
Isaac Newton, Opticks
names the idea; states what it is; opens on it
But in all other curves, the amount of curvature varies from point to point, so that it cannot be measured without infinitesimals. The measure which at once suggests itself is, the curvature of the circle most nearly coinciding with the curve at the point considered. Since a circle is determined by three points, this circle will pass through three consecutive points of the curve. We have thus defined the curvature…
Bertrand Russell, An essay on the foundations of geometry
names the idea; states what it is; opens on it
A somewhat stronger pressure separates the first circle by a slight interval from the imperfectly developed one: it is thus detached, and may be said to appear in a complete state. The centre is now a blue point; for the yellow of the first circle is now separated from this central point by a silver white space. From the centre of the blue a red appears, which is thus, in all cases, bounded on the outside by its…
Johann Wolfgang von Goethe, Goethe's Theory of Colours
names the idea; states what it is; opens on it
In geometry we find a class of proofs in which the successive steps seem to have great significance. A common proof of the area of the circle will serve as a fair example. A regular polygon is circumscribed about the circle. Then as the number of its sides are increased its area will approach that of the circle, as its perimeter approaches the circumference of the circle. The area of the circle is thus inferred to…
John Dewey, Studies in Logical Theory
names the idea; states what it is
Philosophers who discussed Circle
Related ideas
- Greek language
- Archimedes
- Geometry
- Rational number
- Squaring the circle
- Plato
- Euclid's Elements
- Proclus
- Classical antiquity
- Pythagorean theorem
- Science
- Topology
- Triangle
- Dharmachakra
- Western esotericism
- Astronomy
- Calculus
- Creation myth
- Diameter
- Proportionality (mathematics)
- Euclid
- Ellipse
Place in the tradition
Part of Heraclitus.