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Shadows is a software package for the calculation and drawing of sundials and astrolabes, available as a freeware in its base level.. It has been developed by François Blateyron, software developer and amateur astronomer, who made it available on Internet since 1997 and continues to improve it. [1]
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 ...
North African, 9th century CE, planispheric astrolabe. Khalili Collection. A modern astrolabe made in 2013, in Tabriz, Iran.. An astrolabe (Ancient Greek: ἀστρολάβος astrolábos, ' star-taker '; Arabic: ٱلأَسْطُرلاب al-Asṭurlāb; Persian: ستارهیاب Setāreyāb) is an astronomical instrument dating to ancient times.
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
The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.
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 sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.