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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 ...
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]
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 ]
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
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry.In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped ...
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The dual of a linear geometry is obtained by interchanging the roles of points and lines. A survey of linear topological geometries is given in Chapter 23 of the Handbook of incidence geometry. [1] The most extensively investigated topological linear geometries are those which are also dual topological linear geometries.
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