Which beautiful geographic feature can be shaped as Crescentic, Linear, Star, Dome, Parabolic, Longitudinal, Transverse and Reversing?
"linear, star, dome, and parabolic. Dune areas may occur in three forms: simple (isolated dunes of basic type), compound (larger dunes on which smaller dunes of same type form), and complex (combinations of different types). Barchan dunes are crescent-shaped mounds which are generally wider than they are long. The lee-side slipfaces are on the concave sides of the dunes. These dunes form under winds that blow consistently from one direction (unimodal winds). They form separate crescents when the sand supply is comparatively small. When the sand supply is greater, they may merge into barchanoid ridges, and then transverse dunes (see"
"in its historical environment. To calculate what astronomical features a structure faced a coordinate system is needed. The stars provide such a system. If you were to go outside on a clear night you would observe the stars spinning around the celestial pole. This point is +90° if you are watching the North Celestial Pole or −90° if you are observing the Southern Celestial Pole. The concentric circles the stars trace out are lines of celestial latitude, known as ""declination"". The arc connecting the points on the horizon due East and due West (if the horizon is flat) and all"
"stars, domes, parabolas, and longitudinal or seif ('sword') shapes. Barchans or crescent dunes are produced by wind acting on desert sand; the two horns of the crescent and the slip face point downwind. Sand blows over the upwind face, which stands at about 15 degrees from the horizontal, and falls onto the slip face, where it accumulates up to the angle of repose of the sand, which is about 35 degrees. When the slip face exceeds the angle of repose, the sand avalanches, which is a nonlinear behaviour: the addition of many small amounts of sand causes nothing much to"
"be described in terms of 'Latitude' (degrees north or south of the Equator) and Longitude (degrees east or west of the Greenwich Meridian). X is the point where center of celestial body lies on celestial sphere: The Sun, The Moon, The Planets, The Stars. Some of these points appear to move relative to the celestial sphere (The Sun, The Moon, The Planets), but the Stars' declination remain's more or less same as they are very far away but their hour angle(GHA or LHA) change constantly, in fact their hour angle changes by 360 degree in every 23 hour 56 minutes"
"infinite radius). This extension is known as inversive geometry with automorphisms known as ""Mobius transformations"". Second, points are regarded as circles (or spheres) of zero radius. Finally, for technical reasons, the circles (or spheres), including the lines (or planes) are given orientations. These objects, i.e., the points, oriented circles and oriented lines in the plane, or the points, oriented spheres and oriented planes in space, are sometimes called cycles or Lie cycles. It turns out that they form a quadric hypersurface in a projective space of dimension 4 or 5, which is known as the Lie quadric. The natural symmetries"
"the sky. Different cultures have created different groupings of constellations based on differing interpretations of the more-or-less random patterns of dots in the sky. Constellations were identified without regard to distance to each star, but instead as if they were all dots on a dome. Orion is among the most prominent and recognizable constellations. The Big Dipper (which has a wide variety of other names) is helpful for navigation in the northern hemisphere because it points to Polaris, the north star. The pole stars are special because they are approximately in line with the Earth's axis of rotation so they"
"reversal of the east and west constellations (seven constellations of the east have been placed in the west and the seven constellations of the west have been placed in the east). These differences are thought to be due to an error by the painters or because the reproductions of the astronomical directions were erroneous. The stars are painted various sizes, using the Korean tradition of indicating the brightness of the stars. There are 128 stars in total in the painting; some scholars have identified the Big Dipper and either one or several other constellations. A chemical substance and constituent mineral"
"to convex distal lateral edge. Winged crescents are characterized by convex proximal lateral edge and a concave distal lateral edge. Some eccentric crescents have been described as being shaped like animals such as bears, while others consist of serrated or barbed edges. The most common materials crescents are made of include chert, chalcedony, and jasper – all strong and durable lithic materials that are not as brittle as obsidian; however, although its rare, some crescents are made of obsidian. Chipped-stone crescents are found within the western United States, primarily as part of surface assemblages throughout the Great Basin, the Columbia"
"surface. More precisely, the principal curvatures and the mean curvature change the sign if the orientation of the surface is reversed, and the Gaussian curvature is entirely independent of the parametrization. The sign of the Gaussian curvature at a point determines the shape of the surface near that point: for ""K"" > 0 the surface is locally convex and the point is called ""elliptic"", while for ""K"" < 0 the surface is saddle shaped and the point is called ""hyperbolic"". The points at which the Gaussian curvature is zero are called ""parabolic"". In general, parabolic points form a curve on"
"visible. For example, New York City is about 40° north of the equator. The apparent motion of the Sun blots out slightly different parts of the sky from day to day, but over the course of the entire year it sees a dome of 280° (360° - 80°). So for example, both Orion and the Big Dipper are visible during at least part of the year. Making stellar observations from a representative set of points across the Earth, combined with knowing the shortest on-the-ground distance between any two given points makes an approximate sphere the only possible shape for the"
"type is given in the subsections below, along with the effect of the one-parameter subgroup it generates (e.g., on the appearance of the night sky). The Möbius transformations are the conformal transformations of the Riemann sphere (or celestial sphere). Then conjugating with an arbitrary element of SL(2,C) obtains the following examples of arbitrary elliptic, hyperbolic, loxodromic, and parabolic (restricted) Lorentz transformations, respectively. The effect on the flow lines of the corresponding one-parameter subgroups is to transform the pattern seen in the examples by some conformal transformation. For example, an elliptic Lorentz transformation can have any two distinct fixed points on"
"nine parts: the ""first moved"" (""primum mobile""), the sphere of the fixed stars (the firmament), and the seven planets, Saturn, Jupiter, Mars, the sun, Venus, Mercury and the moon. There is a 'right' sphere and an oblique sphere: the right sphere is only observed by those at the equator (if there are such people), everyone else sees the oblique sphere. There are two movements: one of the heavens from east to west on its axis through the Arctic and Antarctic poles, the other of the inferior spheres at 23° in the opposite direction on their own axes. The world, or"
"stable. For example, a distant shoreline may appear to ""tower"" and look higher (and, thus, perhaps closer) than it really is. Because of the turbulence, there appear to be dancing spikes and towers. This type of mirage is also called the Fata Morgana or ""hafgerdingar"" in the Icelandic language. A superior mirage can be right-side up or upside down, depending on the distance of the true object and the temperature gradient. Often the image appears as a distorted mixture of up and down parts. Superior mirages can have a striking effect due to the Earth's curvature. Were the Earth flat,"
"Landform A landform is a natural feature of the solid surface of the Earth or other planetary body. Landforms together make up a given terrain, and their arrangement in the landscape is known as topography. Typical landforms include hills, mountains, plateaus, canyons, and valleys, as well as shoreline features such as bays, peninsulas, and seas, including submerged features such as mid-ocean ridges, volcanoes, and the great ocean basins. Landforms are categorized by characteristic physical attributes such as elevation, slope, orientation, stratification, rock exposure, and soil type. Gross physical features or landforms include intuitive elements such as berms, mounds, hills, ridges,"
"horizon sphere. In the upper half-space model, a horosphere can appear either as a sphere tangent to the horizon plane, or as a plane parallel to the horizon plane. In the hyperboloid model, a horosphere is represented by a plane whose normal lies in the asymptotic cone. A horosphere has a critical amount of (isotropic) curvature: if the curvature were any greater, the surface would be able to close, yielding a sphere, and if the curvature were any less, the surface would be an (""N"" − 1)-dimensional hypercycle. Horosphere In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface"
"a given point, and hyperbolic geometry, in which a line has two parallels and an infinite number of ultraparallels through a given point. An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere. Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided. Concepts of spherical geometry may also be applied to the oblong sphere, though minor modifications must be implemented on certain formulas. Higher-dimensional spherical"
"the horizon. It is one of the largest constellations, with an area of 722 square degrees. This is over 1,400 times the size of the full moon, 55% of the size of the largest constellation, Hydra, and over 10 times the size of the smallest constellation, Crux. Its brightest star, Alpha Andromedae, is a binary star that has also been counted as a part of Pegasus, while Gamma Andromedae is a colorful binary and a popular target for amateur astronomers. Only marginally dimmer than Alpha, Beta Andromedae is a red giant, its color visible to the naked eye. The constellation's"
"various deformations of the Sun's apparent shape soon before sunset or after sunrise. Astronomical refraction deals with the angular position of celestial bodies, their appearance as a point source, and through differential refraction, the shape of extended bodies such as the Sun and Moon. Atmospheric refraction of the light from a star is zero in the zenith, less than 1′ (one arc-minute) at 45° apparent altitude, and still only 5.3′ at 10° altitude; it quickly increases as altitude decreases, reaching 9.9′ at 5° altitude, 18.4′ at 2° altitude, and 35.4′ at the horizon; all values are for 10 °C and"
"forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, have served as an important source of geometric problems throughout history. Modern geometry has many ties to physics as is exemplified by the links between"
"Circumzenithal arc The circumzenithal arc, also called the circumzenith arc (CZA), upside-down rainbow, and the Bravais arc, is an optical phenomenon similar in appearance to a rainbow, but belonging to the family of halos arising from refraction of sunlight through ice crystals, generally in cirrus or cirrostratus clouds, rather than from raindrops. The arc is located at a considerable distance (approximately 46°) above the sun and at most forms a quarter of a circle centered on the zenith. It has been called ""a smile in the sky"", its first impression being that of an upside-down rainbow. The CZA is one"
"fixed points, the North and South poles. The transformations move all other points around latitude circles so that this group yields a continuous counterclockwise rotation about the axis as increases. The ""angle doubling"" evident in the spinor map is a characteristic feature of ""spinorial double coverings"". A hyperbolic element of SL(2,C) is and has fixed points = 0, ∞. Under stereographic projection from the Riemann sphere to the Euclidean plane, the effect of this Möbius transformation is a dilation from the origin. The spinor map converts this to the Lorentz transformation This transformation represents a boost along the axis with"
"only in terms of their relative ratios. As an additional benefit, the concept of contour lines, devised to simplify the process of surveying the mountain, later became a standard technique in cartography. A pendulum hangs straight downwards in a symmetrical gravitational field. However, if a sufficiently large mass such as a mountain is nearby, its gravitational attraction should pull the pendulum's plumb-bob slightly out of true (in the sense that it doesn't point to the centre of mass of the Earth). The change in plumb-line angle against a known object—such as a star—could be carefully measured on opposite sides of"
"these four angles (Ascendant, Descendant, MC or IC). These locations are displayed in the form of lines on the Astro*Carto*Graphy world map. These maps are used by 'astro-cartographers' to counsel their clients on plans for relocation or travel. As such, they are part of a general branch of astrology known as locational astrology or ""relocation astrology"". Other techniques used for this purpose include local space mapping, relocated birth charts, and city incorporation charts. Lewis created the trademark ""Astro*Carto*Graphy"" to refer to his map and granted licenses to three companies to customize his authorized maps and accompanying material: Astro Numeric Services"
"coordinate system, the right ascension coordinates of these borders lie between and , while the declination coordinates are between and . Covering 506 square degrees or 0.921% of the sky, it ranks 31st of the 88 constellations in size. It can be seen at latitudes between +90° and -60° and is best visible at 9 p.m. during the month of March. Cancer Borders the bright constellations of Leo and Gemini and Canis Minor, Under city skies, Cancer is invisible to the naked eye. Cancer is the second dimmest of the zodiacal constellations, having only two stars above the fourth magnitude."
"an ellipse to a parabola or a hyperbola. Sir Isaac Newton showed that a body controlled by the Sun moves in a conic section—that is, an ellipse, a parabola or a hyperbola. Because the latter two are open curves, a comet which pursued such a path would go off into space never to reappear. A derangement of orbit from closed to open curve has doubtless happened often. Great Comet of 1264 The Great Comet of 1264 (C/1264 N1) was one of the brightest comets on record. It appeared in July 1264 and remained visible to the end of September. It"
"northward), and and are east and west lines of longitude (where the angle in radians increases eastward). Mathematically, this represents an arc of angle swept around a sphere by radians. When longitude spans 2 radians and latitude spans radians, the solid angle is that of a sphere. A latitude-longitude rectangle should not be confused with the solid angle of a rectangular pyramid. All four sides of a rectangular pyramid intersect the sphere's surface in great circle arcs. With a latitude-longitude rectangle, only lines of longitude are great circle arcs; lines of latitude are not. The Sun is seen from Earth"
"known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry can be difficult to visualize because Lie transformations do not preserve points in general: points can be transformed into circles (or spheres). To handle this, curves in the plane and surfaces in space are studied using their contact lifts, which are determined by their tangent spaces. This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface. It also allows for a"
"refer to the shape regardless of its orientation, except for the technical language of blazoning used in heraldry, where the word ""increscent"" refers to a crescent shape with its horns to the left, and ""decrescent"" refers to one with its horns to the right, while the word ""crescent"" on its own denotes a crescent shape with horns pointing upward. The shape of the lit side of a spherical body (most notably the Moon) that appears to be less than half illuminated by the Sun as seen by the viewer appears in a different shape from what is generally termed a"
"Dome (geology) A dome is a feature in structural geology consisting of symmetrical anticlines that intersect each other at their respective apices. Intact, domes are distinct, rounded, spherical-to-ellipsoidal-shaped protrusions on the Earth's surface. However, a transect parallel to Earth's surface of a dome features concentric rings of strata. Consequently, if the top of a dome has been eroded flat, the resulting structure in plan view appears as a bullseye, with the youngest rock layers at the outside, and each ring growing progressively older moving inwards. These strata would have been horizontal at the time of deposition, then later deformed by"
"curved and located high above the Sun (or Moon) with its convex side pointing downwards (creating the impression of an ""upside down rainbow""); the circumhorizontal arc runs much closer to the horizon, is more straight and located at a significant distance below the Sun (or Moon). Both arcs have their red side pointing towards the sun and their violet part away from it, meaning the circumzenithal arc is red on the bottom, while the circumhorizontal arc is red on top. The circumhorizontal arc is sometimes referred to by the misnomer ""fire rainbow"". In order to view it, the Sun or"
"presented his geocentric model in the 2nd century. This ""Copernican revolution"" resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent. ""Although Copernicus's groundbreaking book...had been [printed] over a century earlier, [the Dutch mapmaker] Joan Blaeu was the first mapmaker to incorporate his revolutionary heliocentric theory into a map of the world."" Because of Earth's axial tilt (often known as the obliquity of the ecliptic), the inclination of the Sun's trajectory in the sky (as seen by an observer on Earth's surface) varies over the course of the year. For an observer at"
"meaning that elements can be moved throughout the space without changing shape. One of Luneburg's major arguments is that, in accord with a common observation, the transformation involving hyperbolic space renders infinity into a dome (the sky). The Luneburg proposition gave rise to discussions and attempts at corroborating experiments, which on the whole did not favor it. Basic to the problem, and underestimated by Luneburg the mathematician, is the likely success of a mathematically viable formulation of the relationship between objects in physical space and percepts in visual space. Any scientific investigation of visual space is colored by the kind"
"this phenomenon to calculate the Earth's circumference to within of the correct value. The fixed stars can be demonstrated to be very far away, by diurnal parallax measurements (a technique known at least as early as Ancient Greece). Unlike the Sun, Moon, and planets, they do not change position with respect to one another (at least not perceptibly over the span of a human lifetime); the shapes of the constellations are always the same. This makes them a convenient reference background for determining the shape of the Earth. Adding distance measurements on the ground allows calculation of the Earth's size."