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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 ...
Cheng's eigenvalue comparison theorem; Clifford's theorem on special divisors; Cohn-Vossen's inequality; Erdős–Mordell inequality; Euler's theorem in geometry; Gromov's inequality for complex projective space; Gromov's systolic inequality for essential manifolds; Hadamard's inequality; Hadwiger–Finsler inequality; Hinge theorem; Hitchin ...
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
Hindman's theorem (Ramsey theory) Hinge theorem ; Hironaka theorem (algebraic geometry) Hirzebruch signature theorem (topology, algebraic geometry) Hirzebruch–Riemann–Roch theorem (complex manifolds) Hjelmslev's theorem ; Hobby–Rice theorem (mathematical analysis) Hodge index theorem (algebraic surfaces)
The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.
The app allows you to display three Hinge prompt answers, with a myriad of options to choose from (including voice and video prompts!). These range from funny, to deep, to nerdy. The challenge is ...
All Hinge prompts have a 150-character limit, so the idea is to have short, pithy answers that you can elaborate on later. And the word “elaborate” is key here.
For example, the sum of the three angles α + β + γ depends on the size of the triangle. In addition, similar triangles cannot be unequal, so the problem of constructing a triangle with specified three angles has a unique solution.
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