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The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is ...
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) 'upon the circle', meaning "circle moving on another circle") [1] was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets.
A circle of finite radius has an infinitely distant directrix, while a pair of lines of finite separation have an infinitely distant focus. In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.
For elliptical orbits, a simple proof shows that gives the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury ( e = 0.2056 ), one must simply calculate the inverse sine to find the projection angle of 11.86 degrees.
The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.
Eccentric first appeared in English essays as a neologism in 1551, as an astronomical term meaning "a circle in which the earth, sun, etc. deviates from its center." (See Orbital eccentricity.) Five years later, in 1556, an adjective form of the word was used.
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
The Tusi-couple is a mathematical device invented by Nasir al-Din al-Tusi in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.