The trigonometry of a tetrahedron explains the relationships between the lengths and various types of angles of a general tetrahedron. The following are...

solid angles and polytopes such as tetrahedrons and n-simplices. In spherical trigonometry, triangles on the surface of a sphere are studied. The spherical...

theorem Trigonometric function Trigonometry of a tetrahedron Triangle (also see List of triangle topics) Sine, Cosine, Tangent (trigonometric function)...

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six...

Charles (ed.). Elements of Geometry and Trigonometry. New York: A. S. Barnes & Co. p. 197. Stillwell, John (1992). Geometry of Surfaces. Universitext....

Radian Circumference Diameter Trigonometric function Asymptotes Circular functions Periodic functions Law of cosines Law of sines Polar sine Amplitude Dot...

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The...

determine a solid figure called tetrahedron. In non-Euclidean geometries, three "straight" segments (having zero curvature) also determine a "triangle"...

Law of Sines In trigonometry, the law of sines (sometimes called the sine formula or sine rule) is a mathematical equation relating the lengths of the...

Schläfli. As right triangles provide the basis for trigonometry, orthoschemes form the basis of a trigonometry of n dimensions, as developed by Schoute who called...

using trigonometry as below, or the incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular case of acute...

a special case of the more general law of cosines, valid for arbitrary triangles. In a right triangle with sides a, b and hypotenuse c, trigonometry determines...

and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important...

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one...

Inequality Of Diagonal". Archived from the original on 2014-10-24. Retrieved 2011-09-26. C. V. Durell & A. Robson, Advanced Trigonometry, Dover, 2003...

the reciprocal square root of 6. The edge lengths of a regular tetrahedron (t), a regular octahedron (o), and a cube (c) of equal total surface areas satisfy...

of trigonometry and also solved several problems of spherical trigonometry. He was the first whose quantitative and accurate models for the motion of...

any plane containing a bimedian (connector of opposite edges' midpoints) of a tetrahedron bisects the volume of the tetrahedron: pp.89–90  Weisstein,...

define sine, cosine, and π in a way that is totally independent of trigonometry, in which case the proof is valid by the change of variables formula and Fubini's...

height; Tetrahedron – 2 12 a 3 {\textstyle {{\sqrt {2}} \over 12}a^{3}} , where a {\textstyle a} is the side's length. The basic quantities describing a sphere...

referenced to the tetrahedron as volumetric unity. The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the...

essentials of arithmetic, geometry, algebra and trigonometry. McGraw-Hill. p. 422. Alexander Zawaira; Gavin Hitchcock (2009). "Lemma 1: In a right-angled...

one same object, acquiring two images from different points of view. In terms of trigonometry relations, depth information can be calculated from disparity...

with the symmetry groups of regular polyhedra in the three-dimensional Euclidean space: Δ(2,3,3) corresponds to the tetrahedron, Δ(2,3,4) to both the cube...

equal in length, and their symmetries are C4v of order 8 and C5v of order 10, respectively. A tetrahedron or triangular pyramid is an example that has...

algebra, geometry, and trigonometry, the Cayley–Menger determinant is a formula for the content, i.e. the higher-dimensional volume, of a n {\textstyle n} -dimensional...

the volume of a tetrahedron, cylinder, cone, and sphere, for which proofs are given in book XII of Euclid's Elements. In Measurement of a Circle, Archimedes...

puzzle, and the 30-30-120 triangle of the triakis triangular tiling. Five Catalan solids, the triakis tetrahedron, triakis octahedron, tetrakis hexahedron...

publish important results of hyperbolic trigonometry in two papers in 1825 and 1826, yet while admitting the internal consistency of hyperbolic geometry, he...

non-coplanar points A, B, C, and D in 3D form a tetrahedron. In this case, the strict inequality holds: A B ¯ ⋅ C D ¯ + B C ¯ ⋅ D A ¯ > A C ¯ ⋅ B D ¯ {\displaystyle...