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See searches and references containing SPHERICAL CIRCLE!SPHERICAL CIRCLE
Mathematical expression of circle like slices of sphere
spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius)
Spherical_circle
Set of points equidistant from a center
including the parallel postulate. In spherical trigonometry, angles are defined between great circles. Spherical trigonometry differs from ordinary trigonometry
Sphere
Geometry of figures on the surface of a sphere
great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry
Spherical_trigonometry
Concept in geometry
enclosed by a circle of radius R in a flat space is always greater than the area of a spherical circle and smaller than a hyperbolic circle, provided all
Area_of_a_circle
Shortest distance between two points on the surface of a sphere
great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between
Great-circle_distance
Geometry of the surface of a sphere
points and (straight) lines. In spherical geometry, the basic concepts are points and great circles. However, two great circles on a plane intersect in two
Spherical_geometry
Spherical geometry analog of a straight line
arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space
Great_circle
Area on a sphere bounded by two semicircles joined at antipodal points
In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points. It is an
Spherical_lune
Section of a sphere
great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere. The volume of the spherical cap
Spherical_cap
Function used in computer graphics
interpolation parameter represents time, spherical linear interpolation results in a constant-speed motion along a great circle arc between the endpoints or a smooth
Spherical linear interpolation
Spherical_linear_interpolation
Geometric structure
In geometry, the 31 great circles of the spherical icosahedron is an arrangement of 31 great circles in icosahedral symmetry. It was first identified by
31 great circles of the spherical icosahedron
31_great_circles_of_the_spherical_icosahedron
Multiple proofs regarding Earth's approximately spherical shape
The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit
Empirical evidence for the spherical shape of Earth
Empirical_evidence_for_the_spherical_shape_of_Earth
Intersection of a sphere and cone emanating from its center
of the sector of a circle. If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is V = 2 π r
Spherical_sector
Flight or sailing route along the shortest path between two points on a globe's surface
a great circle. Such routes yield the shortest distance between two points on the globe. The great circle path may be found using spherical trigonometry;
Great-circle_navigation
Special mathematical functions defined on the surface of a sphere
sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular
Spherical_harmonics
Portion of a disk enclosed by two radii and an arc
the circle and the two endpoints of the circular arc on the boundary. Conic section Earth quadrant Hyperbolic sector Sector of (mathematics) Spherical sector
Circular_sector
Characterizes spherical triangles with fixed base and area
In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle, called
Lexell's_theorem
In geometry, the 25 great circles of the spherical octahedron is an arrangement of 25 great circles in octahedral symmetry. It was first identified by
25 great circles of the spherical octahedron
25_great_circles_of_the_spherical_octahedron
Perimeter of a circle or ellipse
circumferēns 'carrying around, circling') is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up
Circumference
On tangency patterns of circles
idea of applying a Möbius transformation to a spherical circle packing. The construction obtains a circle packing on a sphere, representing the given graph
Circle_packing_theorem
Straight line segment that passes through the centre of a circle
a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be
Diameter
Family of solutions to related differential equations
solutions are called spherical Bessel functions and are used in spherical systems, such as in solving the Helmholtz equation in spherical coordinates. Bessel's
Bessel_function
Ancient Greek spherical geometry treatise
The Spherics (Greek: τὰ σφαιρικά, tà sphairiká) is a three-volume treatise on spherical geometry written by the Hellenistic mathematician Theodosius of
Theodosius'_Spherics
Archaic conception of Earth's shape
resurgence as a conspiracy theory in the 21st century. The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century
Flat_Earth
Formula for the great-circle distance between two points on a sphere
d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula
Haversine_formula
Property of a planar object which maps onto itself after rotation by any angle
has spherical symmetry in one 3-space, and circular symmetry in the orthogonal direction. An analogous 3-dimensional equivalent term is spherical symmetry
Circular_symmetry
Measure of how closely a shape resembles a sphere
the cross sectional circles along a cylindrical object such as a shaft, is called roundness. Defined by Wadell in 1935, the sphericity, Ψ {\displaystyle
Sphericity
Property of all triangles on a Euclidean plane
B}}={\frac {c}{\sin C}}} . The spherical law of sines deals with triangles on a sphere, whose sides are arcs of great circles. Suppose the radius of the sphere
Law_of_sines
Geographic notion
Gall-Peters projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all circles of latitude are rhumb
Circle_of_latitude
Mathematical relation in spherical triangles
In spherical trigonometry, the law of cosines (or, more specifically, the law of cosines for sides) is a theorem relating the three sides and one of the
Spherical_law_of_cosines
Curve on the sphere analogous to an ellipse or hyperbola
as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant
Spherical_conic
Particular mapping that projects a sphere onto a plane
setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of
Stereographic_projection
multiplied by the anamorphic power of the camera lenses (1× in the case of spherical lenses). Gate dimensions are the width and height of the camera gate aperture
List of motion picture film formats
List_of_motion_picture_film_formats
Geographic coordinate specifying north-south position
latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary
Latitude
Circle-packing on the surface of a sphere
Coulomb energy of electrons in a spherical arrangement. Thus far, solutions have been proven only for small numbers of circles: 3 through 14, and 24. There
Tammes_problem
Problem of constructing equal-area shapes
the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by
Squaring_the_circle
Cylindrical conformal map projection
point the projection uniformly scales the image of a small portion of the spherical surface without otherwise distorting it, preserving angles between intersecting
Mercator_projection
Transparent dry-erase sphere used to teach spherical geometry
scissors A spherical ruler with two scaled edges for drawing great-circle arcs and measuring spherical angles and great-circle distances A spherical compass
Lénárt_sphere
Relation between sides of a right triangle
equation can be derived as a special case of the spherical law of cosines that applies to all spherical triangles: cos c R = cos a R cos b R + sin
Pythagorean_theorem
Method of drawing geometric objects
constructed using compass alone, or by straightedge alone if given a single circle and its center. Ancient Greek mathematicians first conceived straightedge-and-compass
Straightedge and compass construction
Straightedge_and_compass_construction
Measure in 3-dimensional geometry
surface area of a spherical cap is always equal to the area of a circle whose radius equals the distance from the rim of the spherical cap to the point
Solid_angle
Shape with three sides
three "straight" segments also determine a "triangle", for instance, a spherical triangle or hyperbolic triangle. A geodesic triangle is a region of a
Triangle
Non-Euclidean geometry
from spherical geometry by identifying antipodal points of the sphere to a single elliptic point. The elliptic lines correspond to great circles reduced
Elliptic_geometry
Radio telescope located in Guizhou Province, China
The Five-hundred-meter Aperture Spherical Telescope (FAST; Chinese: 五百米口径球面射电望远镜), nicknamed Tianyan (天眼, lit. "Sky's/Heaven's Eye"), is a radio telescope
Five-hundred-meter Aperture Spherical Telescope
Five-hundred-meter_Aperture_Spherical_Telescope
Radius of a circle or sphere equivalent to a non-circular or non-spherical object
mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter
Equivalent_radius
what is essentially spherical trigonometry in the typical Greek form – a geometry or trigonometry of chords in a circle. In the circle in Fig. 10.4 we should
History_of_trigonometry
Model of objects in the sky consisting of a framework of rings
are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting of a spherical framework of
Armillary_sphere
Type of non-Euclidean geometry
horocycle or hypercycle, then the triangle has no circumscribed circle. As in spherical and elliptical geometry, in hyperbolic geometry if two triangles
Hyperbolic_geometry
German mathematician (1826–1866)
to either C {\displaystyle \mathbb {C} } or to the interior of the unit circle. The generalization of the theorem to Riemann surfaces is the famous uniformization
Bernhard_Riemann
Generalization of Pythagorean theorem
arcs of great circles connecting those points. If these great circles make angles A, B, and C with opposite sides a, b, c then the spherical law of cosines
Law_of_cosines
Scottish mathematician (1550–1617)
Wayback Machine Intro to Spherical Trig. Archived 29 March 2006 at the Wayback Machine Includes discussion of The Napier circle and Napier's rules EEBO
John_Napier
Relationship between two lines that meet at a right angle
circle is perpendicular to the tangent line to that circle at the point where the diameter intersects the circle. A line segment through a circle's center
Perpendicular
Area of geometry, about angles and lengths
and he developed spherical trigonometry into its present form. He listed the six distinct cases of a right-angled triangle in spherical trigonometry, and
Trigonometry
SI derived unit of solid angle
surface area of the spherical cap and the square of the sphere's radius. This is analogous to the way a plane angle projected onto a circle delineates a circular
Steradian
Fundamental result in geometry
circle. Pythagoras' theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Spherical
Sum_of_angles_of_a_triangle
Study of geometry using a coordinate system
system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies
Analytic_geometry
Relative distance of a point from a circle
three circles, which touch each other and two sides of the triangle each. Spherical version of Malfatti's problem: The triangle is a spherical one. Essential
Power_of_a_point
Pair of diametrically opposite points on a circle, sphere, or hypersphere
results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle
Antipodal_point
Smooth curves that evenly divide the area of a sphere have at least 4 inflections
A closely related theorem of Segre (1968) also concerns simple closed spherical curves, on spheres embedded into three-dimensional space. If, for such
Tennis_ball_theorem
Geometric pattern used in art
The center of the three-circle figure is called a Reuleaux triangle. Some spherical polyhedra with edges along great circles can be stereographically
Overlapping_circles_grid
Optical device which transmits and refracts light
circle (see each circle of the image in the below figure). The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration
Lens
Equation for radii of tangent circles
of the circles, and not just their radii, to be calculated. With an appropriate definition of curvature, the theorem also applies in spherical geometry
Descartes'_theorem
Imaginary line halfway between Earth's North and South poles
roughly spherical. In spatial (3D) geometry, as applied in astronomy, the equator of a rotating spheroid (such as a planet) is the parallel (circle of latitude)
Equator
theory and quantum computing. The existence and structure of spherical designs on the circle were studied in depth by Hong. Shortly thereafter, Seymour
Spherical_design
Geometric model of the planar projection of the physical universe
also metrical properties induced by a distance, which allows to define circles, and angle measurement. A Euclidean plane with a chosen Cartesian coordinate
Euclidean_plane
Polyhedron with 2 faces
spherical dihedron is made of two spherical polygons which share the same set of n vertices, on a great circle equator; each polygon of a spherical dihedron
Dihedron
Straight figure with zero width and depth
typical example of this. In the spherical representation of elliptic geometry, lines are represented by great circles of a sphere with diametrically opposite
Line_(geometry)
Part of a line that is bounded by two distinct end points; line with two endpoints
vertices, or a diagonal. When the end points both lie on a curve (such as a circle), a line segment is called a chord (of that curve). If V is a vector space
Line_segment
On reflection in a spherical mirror
reflection in a spherical mirror. It asks for the point in the mirror where one given point reflects to another. The special case of a concave spherical mirror
Alhazen's_problem
Property of a mathematical space
having two real dimensions. For example, an ordinary two-dimensional spherical surface, when given a complex metric, becomes a Riemann sphere of one
Dimension
Blurry region in optics
effective focal lengths of different lens zones due to spherical or other aberrations. The term circle of confusion is applied more generally, to the size
Circle_of_confusion
Shape with four equal sides and angles
from four. In spherical geometry, space has uniform positive curvature, and every convex quadrilateral (a polygon with four great-circle arc edges) has
Square
Mathematical space with two coordinates
theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram Square Rectangle Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference
Two-dimensional_space
Differential equation important in physics
translating and summing spherical waves. Let φ(ξ, η, ζ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta
Wave_equation
Area bounded by a circular arc and a straight line
(geometry) Spherical cap Circular sector Mathematics distinguishes when necessary between the words circle and disk: a disk is a plane area having a circle as
Circular_segment
Overview of and topical guide to geometry
Quantum geometry Riemannian geometry Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab
Outline_of_geometry
Part of celestial coordinate system
In astronomy, the hour circle is the great circle through a given object and the two celestial poles. Together with declination and distance (from the
Hour_circle
In-depth exploration of circles, spheres, and inversive geometry by Julian Coolidge
A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge and published
A Treatise on the Circle and the Sphere
A_Treatise_on_the_Circle_and_the_Sphere
Branch of mathematics
Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and
Algebraic_geometry
Direction that Muslims face while praying salah
Francisco, while the great circle method yields 18°51′05″. The great circle model is applied to calculate the qibla using spherical trigonometry—a branch of
Qibla
Branch of mathematics
algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy
Differential_geometry
Directional planes
horizontal take on yet another meaning. On the surface of a smoothly spherical, homogenous, non-rotating planet, the plumb bob picks out as vertical
Vertical_and_horizontal
Triangle in hyperbolic geometry
triangles have some properties that are analogous to those of triangles in spherical or elliptic geometry: Two triangles with the same angle sum are equal
Hyperbolic_triangle
Type of lens
figure at right), and the other one is usually spherical. Such a lens behaves like a combination of a spherical lens and a cylindrical lens. Toric lenses are
Toric_lens
Topological space that locally resembles Euclidean space
-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not self-crossing curves such as a figure-eight. Two-dimensional manifolds
Manifold
Infinitely detailed mathematical structure
games, divination, trade, and architecture. Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Such scaling
Fractal
Geometric model of the physical space
point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there are an infinite number of possible methods.
Three-dimensional_space
Quadrilateral whose vertices lie on a circle
the diagonals intersect. In spherical geometry, a spherical quadrilateral formed from four intersecting greater circles is cyclic if and only if the
Cyclic_quadrilateral
Branch of mathematics
Desargues in the 17th century, all the way back to the implicit use of spherical geometry to understand the Earth's geodesy and to navigate the oceans
Geometry
3-Dimensional analogue of a pendulum
In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass m moving without friction on the surface of a
Spherical_pendulum
Great circle on the celestial sphere that is perpendicular to the horizon
In spherical geometry, a vertical circle is a great circle on the celestial sphere that is perpendicular to the horizon. Therefore, it contains the vertical
Vertical_circle
Fusion power device
A spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or aspect ratio. A traditional
Spherical_tokamak
doi:10.1007/BF01111942 Löwen, R.; Steinke, G.F. (2014), "The circle space of a spherical circle plane", Bull. Belg. Math. Soc. Simon Stevin, 21 (2): 351–364
Topological_geometry
Curve that winds around a central point
the basis for a spherical spiral: draw a straight line on the map and find its inverse projection on the sphere, a kind of spherical curve. One of the
Spiral
Aesthetic quality of blur in the out-of-focus parts of an image
generally a more or less round disc. Depending on how a lens is corrected for spherical aberration, the disc may be uniformly illuminated, brighter near the edge
Bokeh
Problem in geometry
Specifically, the hole has the shape of a right circular cylinder (with two spherical caps) whose axis goes through the center of the sphere. Removing the "hole"
Napkin_ring_problem
Branch of differential geometry and differential topology
theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram Square Rectangle Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference
Symplectic_geometry
Space with one dimension
ambient space in which the line or curve is embedded. Examples include the circle on a plane, or a parametric space curve. In physical space, a 1D subspace
One-dimensional_space
Method for calculating average values
{\text{and }}{\bar {R}}=\|{\bar {x}}\|,} A weighted spherical mean can be defined based on spherical linear interpolation. Center of mass Centroid Circular
Circular_mean
Relation used in geometry
perpendicular. In spherical geometry, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect
Parallel_(geometry)
SPHERICAL CIRCLE
SPHERICAL CIRCLE
Girl/Female
Indian, Tamil
The Sun is the Star at the Centre of the Solar System; It is Almost Perfectly Spherical and Consists of Hot Plasma Interwoven with Magnetic Fields; Sun
Girl/Female
Welsh
Fair. Blessed. White browed. White circle.
Girl/Female
Welsh American
Fair. Blessed. White browed. White circle.
Girl/Female
Hindu
Lord Buddha, Energy circle or a form of chakra
Surname or Lastname
English
English : habitational name from a place in Norfolk, recorded in Domesday Book as Huerueles, named in Old English as hwerflas ‘circles’.
Girl/Female
Latin
Circle of light.
Surname or Lastname
English
English : habitational name from any of the places called Wilby, in Suffolk, Norfolk, and Northamptonshire. The first is probably named from an Old English wilig ‘willow’ + Old English bēag ‘circle’; the second has the same first element + Old Norse býr ‘farmstead’ or Old English bēag, and the last is named with the Old English or Old Scandinavian personal name Villi + býr.
Girl/Female
Hindu
Lord Buddha, Energy circle or a form of chakra
Girl/Female
Welsh
Fair. Blessed. White browed. White circle.
Girl/Female
Tamil
Shaakya | ஷாகà¯à®¯à®¾à®‚
Lord Buddha, Energy circle or a form of chakra
Shaakya | ஷாகà¯à®¯à®¾à®‚
Girl/Female
Welsh
Fair. Blessed. White browed. White circle.
Surname or Lastname
English (Essex, Cambridgeshire)
English (Essex, Cambridgeshire) : possibly a variant of Trendall, a topographic name for someone who lived by a well, earhwork, stone circle, or other circular feature, from Middle English trendel, trandle ‘circle’ (Old English trendel).Possibly an altered spelling of South German Tröndle, a variant of Trendle, a nickname for a tearful person, from Träne ‘tear’ + the diminutive suffix -l.
Girl/Female
Japanese
Ball; circle.
Girl/Female
Welsh American
Fair. Blessed. White browed. White circle.
Boy/Male
French Israeli
The circle.
Girl/Female
Welsh Arthurian Legend Celtic
Fair. Blessed. White browed. White circle.
Girl/Female
Latin
Circle of light.
Girl/Female
Latin
Circle of light.
Surname or Lastname
English, German, and Dutch
English, German, and Dutch : metonymic occupational name for a maker of rings (from Middle English ring, Middle High German rinc, Middle Dutch ring), either to be worn as jewelry or as component parts of chain-mail, harnesses, and other objects. In part it may also have arisen as a nickname for a wearer of a ring.Scandinavian : from ring ‘ring’, probably an ornamental name but possibly applied in the same sense as 3 or 1.German : topographic name from Middle High German, Middle Low German rink, rinc ‘circle’.Irish (eastern County Cork) : reduced Anglicized form of Gaelic Ó Rinn (see Reen).
Girl/Female
Tamil
Lord Buddha, Energy circle or a form of chakra
SPHERICAL CIRCLE
SPHERICAL CIRCLE
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
King of Gems
Girl/Female
Hindu, Indian
Beautiful Eyes
Boy/Male
Hindu
Baby Krishna, Infant Krishna
Boy/Male
Tamil
First, Most important, Beginning, Ornament, Adornment
Girl/Female
Tamil
Goddess Sita
Boy/Male
Tamil
Lord Krishna
Girl/Female
Muslim
Indestructible
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Full of Love
Boy/Male
Indian, Tamil
Little Boy
Girl/Female
Tamil
Hemangni | ஹேமஂகநீÂ
Girl with golden body
SPHERICAL CIRCLE
SPHERICAL CIRCLE
SPHERICAL CIRCLE
SPHERICAL CIRCLE
SPHERICAL CIRCLE
v. t.
To form into roundness; to make spherical, or spheral; to perfect.
n.
A rudimentary form of crystallite, spherical in shape.
adv.
Spherically.
a.
Alt. of Schetical
a.
Spherical; orbicular; orblike; circular.
a.
Exactly spherical; globular.
a.
Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.
a.
Round; circular; spherical.
a.
Made convex; protuberant in a spherical form.
a.
Globular; spherical; orbicular.
a.
Having the form of a bunch of grapes; like a cluster of grapes, as a mineral presenting an aggregation of small spherical or spheroidal prominences.
a.
See Spheroidal.
n.
The eye, as luminous and spherical.
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
n.
Freedom from spherical aberration.
a.
Round; spherical; starlike.
a.
Alt. of Spheric
n.
A portion of a spherical or other convex surface.
a.
Having the form of a globe; spherical.
a.
Spherical.