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Theorem in Riemannian geometry
In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics
Sphere_theorem
Statement on the gravitational attraction of spherical bodies
theorem (2). But the point can be considered to be external to the remaining sphere of radius r, and according to (1) all of the mass of this sphere can
Shell_theorem
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
Pathological embedding of the sphere in 3D space
that can "straighten" the horned sphere into a standard sphere. In the late 19th century, the Jordan curve theorem established that every simple closed
Alexander_horned_sphere
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the
Uniformization_theorem
German mathematician
(conjectured by Richard Hamilton). In 2007, he proved the differentiable sphere theorem (in collaboration with Richard Schoen), a fundamental problem in global
Simon_Brendle
Mathematical space
Papakyriakopoulos in 1956, along with Dehn's lemma and the Sphere theorem. A simple and useful version of the loop theorem states that if there is a map f : ( D 2 , ∂
3-manifold
Theorem in topology
higher dimensions (see below). Formally, the theorem states that every continuous function from an n-sphere into n-dimensional Euclidean space must map
Borsuk–Ulam_theorem
On when elements of the 2nd homotopy group of a 3-manifold can be embedded spheres
In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos (1957) gives conditions for elements of the second homotopy
Sphere_theorem_(3-manifolds)
American mathematician (born 1950)
obtaining a new convergence theorem for Ricci flow. A special case of their convergence theorem has the differentiable sphere theorem as a simple corollary
Richard_Schoen
On when a manifold that admits a singular foliation is homeomorphic to the sphere
In mathematics, Reeb sphere theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having
Reeb_sphere_theorem
Equation for radii of tangent circles
theorem to spheres, and in another poem described the chain of six spheres each tangent to its neighbors and to three given mutually tangent spheres,
Descartes'_theorem
Generalization of Dehn's lemma in the topology of 3-manifolds
Papakyriakopoulos in 1956, along with Dehn's lemma and the Sphere theorem. A simple and useful version of the loop theorem states that if for some 3-dimensional manifold
Loop_theorem
Theorem that any three objects in space can be simultaneously bisected by a plane
convergence theorem). By the Borsuk–Ulam theorem, there are antipodal points v {\displaystyle v} and − v {\displaystyle -v} on the sphere S such that
Ham_sandwich_theorem
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used
Poincaré–Hopf_theorem
Theorem in differential geometry
northern hemisphere cut out from a sphere of radius R. Its Euler characteristic is 1. On the left hand side of the theorem, we have K = 1 / R 2 {\displaystyle
Gauss–Bonnet_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Spheres tangent to a plane inside a cone
well. The Dandelin spheres can be used to give elegant modern proofs of two classical theorems known to Apollonius. The first theorem is that a closed conic
Dandelin_spheres
geometry) Soul theorem (Riemannian geometry) Sphere theorem (Riemannian geometry) Synge's theorem (Riemannian geometry) Toponogov's theorem (Riemannian geometry)
List_of_theorems
Set of points equidistant from a center
Euclid does not include the area and volume of a sphere, only a theorem that the volume of a sphere varies as the third power of its diameter, probably
Sphere
Theorem in geometric topology
/ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds the 4-ball in four-dimensional
Poincaré_conjecture
Result on the topology of operators on an infinite-dimensional, complex Hilbert space
In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H
Kuiper's_theorem
Theorem in topology
resulting in the Jordan–Brouwer separation theorem. Theorem—Let X be an n-dimensional topological sphere in the (n+1)-dimensional Euclidean space Rn+1
Jordan_curve_theorem
Russian mathematician (born 1966)
cylinder collapsing to its axis, or a sphere collapsing to its center. Perelman's proof of his canonical neighborhoods theorem is a highly technical achievement
Grigori_Perelman
Theorem on the behavior of dynamical systems
Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere. Given a
Poincaré–Bendixson_theorem
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
How spheres of various dimensions can wrap around each other
approximation theorem. When i = n, every map from Sn to itself can be assigned a degree that intuitively measures how many times the sphere is wrapped around
Homotopy_groups_of_spheres
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Partial differential equation
convergence theorem (Brendle & Schoen 2009). Their convergence theorem included as a special case the resolution of the differentiable sphere theorem, which
Ricci_flow
Russian-French mathematician
the notion of almost flat manifolds.[G78] The famous quarter-pinched sphere theorem in Riemannian geometry says that if a complete Riemannian manifold has
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
German mathematician
major achievements was the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a complete, simply connected
Wilhelm_Klingenberg
Results on the surface areas and volumes of surfaces and solids of revolution
Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with
Pappus's_centroid_theorem
Representation of a quantum mechanical system
In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit)
Bloch_sphere
Branch of differential geometry
manifold or on the behavior of points at "sufficiently large" distances. Sphere theorem. If M is a simply connected compact n-dimensional Riemannian manifold
Riemannian_geometry
Existence of geodesic circles on surfaces
the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has
Theorem of the three geodesics
Theorem_of_the_three_geodesics
On the intersection form of a smooth, closed 4-manifold with a spin structure
\Sigma } to be any small sphere, which has self intersection number 0, so Rokhlin's theorem follows. The Freedman–Kirby theorem (Freedman & Kirby 1978)
Rokhlin's_theorem
Model of the extended complex plane plus a point at infinity
curvature in any given conformal class. In the case of the Riemann sphere, the Gauss–Bonnet theorem implies that a constant-curvature metric γ {\displaystyle \gamma
Riemann_sphere
Every Riemannian manifold can be isometrically embedded into some Euclidean space
Nash–Kuiper theorem. For example, the image of any smooth isometric hypersurface immersion of the round sphere must itself be a round sphere. By contrast
Nash_embedding_theorems
rings Newton's rotating sphere argument, see rotating spheres Newton scale Newton's sphere theorem, see shell theorem Newton's theorem of revolving orbits
List of things named after Isaac Newton
List_of_things_named_after_Isaac_Newton
Theorem in topology
using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem. Papakyriakopoulos proved Dehn's lemma using a tower
Dehn's_lemma
Geometrical concept relating area and volume
able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi
Cavalieri's_principle
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Extends the Jordan curve theorem to characterize the inner and outer regions
the unit circle. To prove the theorem, Carathéodory's theorem can be applied to the two regions on the Riemann sphere defined by the Jordan curve. This
Schoenflies_problem
American mathematician (1943–2024)
convergence theorems of Hamilton were extended by Simon Brendle and Richard Schoen in 2009 to give a proof of the differentiable sphere theorem, which had
Richard_S._Hamilton
On tangency patterns of circles
tangencies, and the circle packing theorem, have been extended to arbitrary Riemannian surfaces including the sphere, the hyperbolic plane, and to surfaces
Circle_packing_theorem
conjecture (in the positive curvature case) follows from the sphere theorem, a theorem which had also been conjectured first by Hopf. One of the lines
Hopf_conjecture
One-dimensional complex manifold
global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. Examples of Riemann surfaces
Riemann_surface
Key results in general relativity on gravitational singularities
when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Dehn's lemma Loop theorem (aka the Disk theorem) Sphere theorem Haken manifold JSJ decomposition Branched surface Lamination Examples 3-sphere Torus bundles
List of geometric topology topics
List_of_geometric_topology_topics
Topological operation of turning a sphere inside-out without creasing
Nylon string open model Whitney–Graustein theorem Bednorz, Adam; Bednorz, Witold (2019). "Analytic sphere eversion using ruled surfaces". Differential
Sphere_eversion
Concept in topology
hard open question of whether the 4-sphere has non-standard smooth structures. For n = 2, the h-cobordism theorem is equivalent to the Poincaré conjecture
H-cobordism
Field of higher mathematics
Riemannian Geometry: A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem (1st ed.). Springer. ISBN 978-3-642-16285-5. Jost, Jürgen (2005). Riemannian
Geometric_analysis
Existence of antipodal pairs in covers of spheres
the subset. The Lusternik–Schnirelmann theorem can then be stated as: Lusternik–Schnirelmann theorem—If the sphere S n {\displaystyle S^{n}} is covered
Lusternik–Schnirelmann theorem
Lusternik–Schnirelmann_theorem
Mathematical result in differential geometry
index. By taking Y to be some sphere that X embeds in, this reduces the index theorem to the case of spheres. If Y is a sphere and X is some point embedded
Atiyah–Singer_index_theorem
Theorem in plane geometry
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others
Monge's_theorem
Theorem in geometry
In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures)
Brunn–Minkowski_theorem
Smooth curves that evenly divide the area of a sphere have at least 4 inflections
In geometry, the tennis ball theorem states that any smooth curve on the surface of a sphere that divides the sphere into two equal-area subsets without
Tennis_ball_theorem
Geometric theorem
The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists
Banach–Tarski_paradox
Foundational law of electromagnetism relating electric field and charge distributions
as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the
Gauss's_law
French mathematician (1920–1993)
particular, the Reeb sphere theorem says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. In turn, in 1956
Georges_Reeb
Analyzes the topology of a manifold by studying differentiable functions on that manifold
studied by Georges Reeb in 1952; the Reeb sphere theorem states that M {\displaystyle M} is homeomorphic to a sphere S n . {\displaystyle S^{n}.} The case
Morse_theory
Limitation on the minimum time for a quantum system to evolve between two states
{\displaystyle \left|\psi \right\rangle .} (This is the quarter-pinched sphere theorem in disguise, transported to complex projective space.) Thus, one has
Quantum_speed_limit
soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature. The theorem was proven in
Alexandrov's soap bubble theorem
Alexandrov's_soap_bubble_theorem
Mathematical concept
and is the roundest manifold that is not a sphere (or covered by a sphere): by the 1/4-pinched sphere theorem, any complete, simply connected Riemannian
Complex_projective_space
Hypothetical megastructure around a star
fiction, Dyson spheres present engineering challenges that complicate their use in storytelling. One such difficulty arises from the shell theorem: within a
Dyson_sphere
Movement with a fixed point is rotation
would look like if the theorem were true. To that end, suppose the yellow line in Figure 1 goes through the center of the sphere and is the axis of rotation
Euler's_rotation_theorem
Graph that can be embedded in the plane
conditions hold for v ≥ 3: Theorem 1. e ≤ 3v − 6; Theorem 2. If there are no cycles of length 3, then e ≤ 2v − 4. Theorem 3. f ≤ 2v − 4. In this sense
Planar_graph
of each dimension for a simplicial d-sphere? In the case of polytopal spheres, the answer is given by the g-theorem, proved in 1979 by Billera and Lee (existence)
Simplicial_sphere
Product of the principal curvatures of a surface
even a small part of a sphere must distort the distances. Therefore, no cartographic projection is perfect. The Gauss–Bonnet theorem relates the total curvature
Gaussian_curvature
Characterizes spherical triangles with fixed base and area
corresponding apex. Two points on a sphere are antipodal if they are diametrically opposite, as far apart as possible. The theorem is named for Anders Johan Lexell
Lexell's_theorem
Three-dimensional packing problem
Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It
Sphere_packing_in_a_sphere
Topological degree is the only homotopy invariant of continuous maps to spheres
The Hopf theorem (named after Heinz Hopf) is a statement in differential topology, saying that the topological degree is the only homotopy invariant of
Hopf_theorem
American mathematician
1960s. This optimal result is known as the sphere theorem for Riemannian manifolds. The Rauch comparison theorem is also named after Harry Rauch. He proved
Harry_Rauch
Two-dimensional manifold
classification theorem of closed surfaces states that any connected closed surface is homeomorphic to some member of one of these three families: the sphere, the
Surface_(topology)
German mathematician (1894–1971)
to the Euler characteristic of the manifold. This theorem is now called the Poincaré–Hopf theorem. Hopf spent the year after his doctorate at the University
Heinz_Hopf
2-dimensional complex projective space
so. That is, it attains both bounds and thus evades being a sphere, as the sphere theorem would otherwise require. The rival normalisations are for the
Complex_projective_plane
Characterizes complete connected Riemannian manifolds of constant curvature
Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space
Killing–Hopf_theorem
Topics referred to by the same term
Poincaré theorem may refer to: Poincaré conjecture, on homeomorphisms to the sphere; Poincaré recurrence theorem, on sufficient conditions for recurrence
Poincaré_theorem
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
Theorem in vector calculus
theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,
Stokes'_theorem
Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature
{\displaystyle \gamma _{n}} is the surface area of the unit n-sphere. The Gauss–Bonnet theorem is a special case when M {\displaystyle M} is a 2-dimensional
Chern–Gauss–Bonnet_theorem
Two pentagonal pyramids fused base-to-base
1016/j.dam.2009.08.002, MR 2602814. Knill, Oliver (2019), A Simple Sphere Theorem for Graphs, arXiv:1910.02708. Montroll, John (2011), Origami Polyhedra
Pentagonal_bipyramid
Theorem in quantum mechanics
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from
Gleason's_theorem
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
When curves on a surface passing through a given point have the same normal curvature
the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776, but not published
Meusnier's_theorem
Two tame knots with homeomorphic complements are the same or mirror images
called the Gordon–Luecke theorem): no nontrivial Dehn surgery on a nontrivial knot in the 3-sphere can yield the 3-sphere. The theorem was proved by Cameron
Gordon–Luecke_theorem
Graph-theoretic description of polyhedra
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices
Steinitz's_theorem
Smooth 4-manifold homeomorphic yet not diffeomorphic to Euclidean space
by using the contrast between Freedman's theorems about topological 4-manifolds, and Simon Donaldson's theorems about smooth 4-manifolds. There is a continuum
Exotic_R4
projective space. In this way, it can be viewed as an analogue of the sphere theorem in Riemannian geometry, which (in a weak form) states that if a closed
Frankel_conjecture
Poincaré–Hopf theorem Stokes' theorem De Rham cohomology Sphere eversion Frobenius theorem (differential topology) Distribution (differential geometry)
List of differential geometry topics
List_of_differential_geometry_topics
Smooth manifold that is homeomorphic but not diffeomorphic to a sphere
essentially unique smooth structure (see Moise's theorem), so the monoid of smooth structures on the 3-sphere is trivial. The group Θ n {\displaystyle \Theta
Exotic_sphere
is aspherical. The complement of a knot in S3 is aspherical, by the sphere theorem Complete metric spaces with nonpositive curvature in the sense of Aleksandr
Aspherical_space
Concerns 3 circles through triples of points on the vertices and sides of a triangle
G. Wells refers to this as Miquel's theorem. There is also a three-dimensional analog, in which the four spheres passing through a point of a tetrahedron
Miquel's_theorem
Danish-American mathematician
recognized mathematical contributions to Riemannian Geometry is the Diameter Sphere Theorem, proved jointly with Katsuhiro Shiohama in 1977, which states that a
Karsten_Grove
Overview of and topical guide to geometry
Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini
Outline_of_geometry
Math theorem about sphere packing
mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space
Kepler_conjecture
Convex polyhedron with 14 triangle faces
pp. 181–182, ISBN 978-0-387-74640-1. Knill, Oliver (2019), A simple sphere theorem for graphs, arXiv:1910.02708. Fomin, Sergey; Reading, Nathan (2007)
Triaugmented_triangular_prism
How many linearly independent smooth nowhere-zero vector fields can be on an n-sphere
discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification
Vector_fields_on_spheres
Doughnut-shaped surface of revolution
must lie strictly outside the sphere, which is a contradiction.) On the other hand, according to the Nash-Kuiper theorem, which was proven in the 1950s
Torus
Topological manifold whose homology coincides with that of a sphere
Hurewicz theorem). A rational homology sphere is defined similarly but using homology with rational coefficients. The Poincaré homology sphere (also known
Homology_sphere
SPHERE THEOREM
SPHERE THEOREM
Girl/Female
French, German, Hebrew
Beloved; A Man; The Plain
Surname or Lastname
English
English : topographic name for someone who lived by the seashore, Middle English schore.English : topographic name for someone who lived on or by a bank or steep slope, Old English scora. There are minor places named with this word in Lancashire and West Yorkshire, and the surname may also be a habitational name from these.Americanized spelling of Ashkenazic Jewish S(c)hor(r) or Szor, variants of Schauer.
Boy/Male
American, British, English
Spear
Surname or Lastname
English
English : variant of Spear.
Male
English
Variant spelling of English Ophir, OPHER means "gold" or "reducing to ashes."
Male
Hebrew
(עֵפֶר) Hebrew name EPHER means "calf" or "gazelle." In the bible, this is the name of several characters, including a son of Ezra.
Girl/Female
American, Christian, French, German, Hebrew
Darling; Little and Womanly; Beloved; The Plain
Female
English
Variant spelling of English Sherry, SHERIE means "darling."
Boy/Male
British, English
Spear-man
Surname or Lastname
English and Irish (County Limerick; of English origin)
English and Irish (County Limerick; of English origin) : from Old English scīr, Middle English s(c)hire ‘shire’, perhaps a topographic name for someone who lived by the meeting place of a shire.
Female
English
Variant spelling of English Sherry, SHEREE means "darling."
Female
English
Variant spelling of English Sherry, SHERI means "darling."
Boy/Male
Australian, French, Portuguese
Stern; Severe
Girl/Female
Indian, Telugu
Veda means Vedham and Shree means Sriman Narayana
Surname or Lastname
English
English : variant spelling of Shear 1.Indian (Maharashtra); pronounced as two syllables : Hindu (Vani) name, probably from Marathi šera ‘rate’.
Surname or Lastname
English
English : variant of Shear 1.Jewish (eastern Ashkenazic) : variant spelling of Scher.
Surname or Lastname
English
English : variant of Sherrin.
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Girl/Female
French, German, Hebrew
Little and Womanly; Dear; Man; The Plain
Female
English
English variant spelling of Greek Phoebe, PHEBE means "shining one."
SPHERE THEOREM
SPHERE THEOREM
Boy/Male
British, English, German
Bright Angel
Male
Irish
Irish Gaelic name DAITHÃ means "swift."
Girl/Female
Hindu, Indian
Generosity; Passing Clouds
Girl/Female
Arabic, Muslim
Excellence of the Women
Girl/Female
Australian, Portuguese
Fern
Girl/Female
Hindu, Indian
Wife of King
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Sun Rays; Sun; Patience
Girl/Female
Indian
Sweet and Lovely
Girl/Female
Hindu
Decorative, Name of a river
Boy/Male
Tamil
Mine of nectar
SPHERE THEOREM
SPHERE THEOREM
SPHERE THEOREM
SPHERE THEOREM
SPHERE THEOREM
v. t.
To place in a sphere, or among the spheres; to insphere.
imp. & p. p.
of Sphere
n.
The apparent surface of the heavens, which is assumed to be spherical and everywhere equally distant, in which the heavenly bodies appear to have their places, and on which the various astronomical circles, as of right ascension and declination, the equator, ecliptic, etc., are conceived to be drawn; an ideal geometrical sphere, with the astronomical and geographical circles in their proper positions on it.
adv.
In this place; in the place where the speaker is; -- opposed to there.
a.
Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.
n.
A sphere.
v. t.
To place in a sphere; to envelop.
v. t.
To form into roundness; to make spherical, or spheral; to perfect.
superl.
Sharp; afflictive; distressing; violent; extreme; as, severe pain, anguish, fortune; severe cold.
v. i.
To form a scheme or schemes.
a.
Of or pertaining to a sphere or the spheres.
n.
A sphere or scheme of operation.
a.
Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set.
v. t.
To place in, or as in, an orb a sphere. Cf. Ensphere.
v. t.
To form into a sphere.
n.
A sphere.
a.
Of or pertaining to the spheres.
a.
Rounded like a sphere; sphere-shaped; hence, symmetrical; complete; perfect.
a.
Of or pertaining to a sphere.
v. t.
To remove, as a planet, from its sphere or orb.