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  2. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap ...

  3. Convex cap - Wikipedia

    en.wikipedia.org/wiki/Convex_cap

    The definition of a cap can also be extended to define a cap of a point where the cap can be defined as the intersection of a convex set with a half-space containing . The minimal cap of a point is a cap of x {\displaystyle x} with vol ⁡ ( C ( x ) ) = min ⁡ { vol ⁡ ( K ∩ H ) : x ∈ H } {\displaystyle \operatorname {vol} (C(x ...

  4. Solid angle - Wikipedia

    en.wikipedia.org/wiki/Solid_angle

    Over 2200 years ago Archimedes proved that the 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 where the cap's axis of symmetry intersects the cap. [3] Archimedes' theorem that surface area of the region of sphere below horizontal plane H in ...

  5. CAP theorem - Wikipedia

    en.wikipedia.org/wiki/CAP_theorem

    Note that consistency as defined in the CAP theorem is quite different from the consistency guaranteed in ACID database transactions. [4] Availability Every request received by a non-failing node in the system must result in a response. This is the definition of availability in CAP theorem as defined by Gilbert and Lynch. [1]

  6. Intersection (set theory) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(set_theory)

    Intersection (Euclidean geometry) – Shape formed from points common to other shapes; Intersection graph – Graph representing intersections between given sets; Intersection theory – Branch of algebraic geometry; List of set identities and relations – Equalities for combinations of sets

  7. (G, X)-manifold - Wikipedia

    en.wikipedia.org/wiki/(G,_X)-manifold

    In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds.

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Descartes's theorem (plane geometry) Descartes's theorem on total angular defect ; Diaconescu's theorem (mathematical logic) Diller–Dress theorem (field theory) Dilworth's theorem (combinatorics, order theory) Dinostratus' theorem (geometry, analysis) Dimension theorem for vector spaces (vector spaces, linear algebra) Dini's theorem

  9. Cap set - Wikipedia

    en.wikipedia.org/wiki/Cap_set

    In affine geometry, a cap set is a subset of the affine space (the -dimensional affine space over the three-element field) where no three elements sum to the zero vector. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of n {\displaystyle n} . [ 1 ]

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