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searching for Hyperbolic triangle 18 found (45 total)

Hyperbolic sector (829 words) [view diff] exact match in snippet view article find links to article

former. When in standard position, a hyperbolic sector determines a hyperbolic triangle, the right triangle with one vertex at the origin, base on the diagonal

Non-Euclidean crystallographic group (154 words) [view diff] exact match in snippet view article find links to article

index 2 Fuchsian subgroup of orientation-preserving elements. The hyperbolic triangle groups are notable NEC groups. Others are listed in Orbifold notation

Hyperbolic angle (2,276 words) [view diff] exact match in snippet view article find links to article

trigonometric functions by regarding a hyperbolic angle as defining a hyperbolic triangle. The parameter thus becomes one of the most useful in the calculus

(2,3,7) triangle group (818 words) [view diff] exact match in snippet view article

First Hurwitz triplet. To construct the triangle group, start with a hyperbolic triangle with angles π/2, π/3, and π/7. This triangle, the smallest hyperbolic

Order-3 apeirogonal tiling (327 words) [view diff] exact match in snippet view article find links to article

Regular Truncations {∞,3} t0,1{∞,∞} t1,2{∞,∞} t{∞[3]} Hyperbolic triangle groups [∞,3] [∞,∞] [(∞,∞,∞)]

Modular group (3,317 words) [view diff] exact match in snippet view article find links to article

= 1/2 and Re(z) = −1/2, and the circle |z| = 1. This region is a hyperbolic triangle. It has vertices at 1/2 + i√3/2 and −1/2 + i√3/2, where the angle

Normalizing constant (1,010 words) [view diff] exact match in snippet view article find links to article

and sinh from the lengths of the adjacent and opposite sides of a hyperbolic triangle. Normalization (statistics) Continuous Distributions at University

Systoles of surfaces (924 words) [view diff] exact match in snippet view article find links to article

defined by a tower of principal congruence subgroups of the (2,3,7) hyperbolic triangle group satisfy the bound sys(Σg)≥43log⁡g,{\displaystyle \mathrm {sys}

Right triangle (2,951 words) [view diff] exact match in snippet view article find links to article

hyperbolic functions as ratio of the sides of a right triangle, see the hyperbolic triangle of a hyperbolic sector. The values of the trigonometric functions

Uniform tilings in hyperbolic plane (1,586 words) [view diff] exact match in snippet view article find links to article

points of the fundamental domain triangle – the symmetry group is a hyperbolic triangle group. Each symmetry family contains 7 uniform tilings, defined by

Schwarz's list (904 words) [view diff] no match in snippet view article find links to article

Another relevant list is that of K. Takeuchi, who classified the (hyperbolic) triangle groups that are arithmetic groups (85 examples). Émile Picard sought

Coxeter group (3,588 words) [view diff] exact match in snippet view article find links to article

describing reflection groups in hyperbolic space, notably including the hyperbolic triangle groups. A Coxeter group is said to be irreducible if its Coxeter–Dynkin

Systolic geometry (3,932 words) [view diff] exact match in snippet view article find links to article

defined by a tower of principal congruence subgroups of the (2,3,7) hyperbolic triangle group satisfy the bound s y s π 1 ( Σ g ) ≥ 4 3 log ⁡ g , {\displaystyle

Triangle center (3,898 words) [view diff] exact match in snippet view article find links to article

Applications. 6 (1): 1–35., article #18 Ungar, Abraham A. (2010). Hyperbolic triangle centers : the special relativistic approach. Dordrecht: Springer

Klein quartic (3,288 words) [view diff] exact match in snippet view article find links to article

algebraic integers. The group Γ(I) is a subgroup of the (2,3,7) hyperbolic triangle group. Namely, Γ(I) is a subgroup of the group of elements of unit

Mass in special relativity (6,288 words) [view diff] case mismatch in snippet view article find links to article

December 12, 2017 – via HUIT Sites Hosting. Ungar, Abraham A. (2010). Hyperbolic Triangle Centers: The Special Relativistic Approach. Dordrecht: Springer.

Orbifold (10,240 words) [view diff] exact match in snippet view article find links to article

2-dimensional orbifold. The corresponding group is an example of a hyperbolic triangle group. Poincaré also gave a 3-dimensional version of this result

List of uniform polyhedra by Schwarz triangle (2,757 words) [view diff] exact match in snippet view article find links to article

Möbius triangle as well; but this is impossible as (2 4 5) is a hyperbolic triangle, not a spherical one.) Apart from the octahemioctahedron, the hemipolyhedra