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Girih patterns can be created in a variety of ways, including the traditional straightedge and compass construction; the construction of a grid of polygons; and the use of a set of girih tiles with lines drawn on them: the lines form the pattern. Patterns may be elaborated by the use of two levels of design, as at the 1453 Darb-e Imam shrine.
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space.Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.
Geodesy is formatted as a textbook on the topic of geodesy, with particular emphasis on its applications to triangulation. For content on applied geodesy, it is assumed the reader can use a theodolite and a micrometer. The book also discusses the overlap between geodesy and the study of geophysics. [3]
A number of pattern books have been very influential in spreading architectural styles. An early author of pattern books was American architect Minard Lafever. In 1829 he published The Young Builders' General Instructor, followed by Modern Builders' Guide in 1833, The Beauties of Modern Architecture in 1835 and The Architectural Instructor in 1850.
Online geodesic bibliography of books and articles on geodesics on ellipsoids. Test set for geodesics, a set of 500000 geodesics for the WGS84 ellipsoid, computed using high-precision arithmetic. NGS tool implementing Vincenty (1975). geod(1), man page for the PROJ utility for geodesic calculations. GeographicLib implementation of Karney (2013).
The shortest path between two points on a spheroid is known as a geodesic. Such paths are developed using differential geometry. The equator and meridians are great ellipses that are also geodesics [a]. The maximum difference in length between a great ellipse and the corresponding geodesic of length 5,000 nautical miles is about 10.5 meters.