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Since the planisphere shows the celestial sphere in a printed flat, there is always considerable distortion. Planispheres, like all charts, are made using a certain projection method. For planispheres there are two major methods in use, leaving the choice with the designer. One such method is the polar azimuthal equidistant projection. Using ...
"there is no convincing evidence that Ptolemy or any of his predecessors knew about the planispheric astrolabe". [14] In chapter 5.1 of the Almagest, Ptolemy describes the construction of an armillary sphere, and it is usually assumed that this was the instrument he used. Astrolabes continued to be used in the Byzantine Empire.
Planisphere or Planisphaerium, a 2nd-century AD book by Claudius Ptolemy about mapping the celestial sphere onto a flat plane using the stereographic projection to make a star chart; Planispheric astrolabe, a device consisting of a planisphere joined to a dioptra, used for observing stars and performing astronomical calculations
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
The fundamental plane in a spherical coordinate system is a plane of reference that divides the sphere into two hemispheres. The geocentric latitude of a point is then the angle between the fundamental plane and the line joining the point to the centre of the sphere. [1] For a geographic coordinate system of the Earth, the fundamental plane is ...
In Greek antiquity the ideas of celestial spheres and rings first appeared in the cosmology of Anaximander in the early 6th century BC. [7] In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...