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The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
Minkowski's first inequality for convex bodies; Myers's theorem; Noether inequality; Ono's inequality; Pedoe's inequality; Ptolemy's inequality; Pu's inequality; Riemannian Penrose inequality; Toponogov's theorem; Triangle inequality; Weitzenböck's inequality; Wirtinger inequality (2-forms)
The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following: [1] [2] Three sides (SSS) Two sides and the included angle (SAS, side-angle-side)
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element in a Hilbert space with respect to an orthonormal sequence. The inequality was derived by F.W. Bessel in 1828.
Here are some of the best Hinge prompt answers. ... Royals agree to 3-year, $13.25M contract. Weather. Weather. Fox Weather. Avalanche buries 2 ski patrollers on California’s Sierra Nevada.
If S is a compact surface (without boundary), then the inequality is an equality by the usual Gauss–Bonnet theorem for compact manifolds. If S has a boundary, then the Gauss–Bonnet theorem gives ∬ S K d A = 2 π χ ( S ) − ∫ ∂ S k g d s {\displaystyle \iint _{S}K\,dA=2\pi \chi (S)-\int _{\partial S}k_{g}\,ds}
and this inequality is strict whenever the convergence is not strong. For example, infinite orthonormal sequences converge weakly to zero, as demonstrated below. If x n → x {\displaystyle x_{n}\to x} weakly and ‖ x n ‖ → ‖ x ‖ {\displaystyle \lVert x_{n}\rVert \to \lVert x\rVert } , then x n → x {\displaystyle x_{n}\to x} strongly: