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Ideal triangle information


Three ideal triangles in the Poincaré disk model creating an ideal pentagon
Two ideal triangles in the Poincaré half-plane model

In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points. Ideal triangles are also sometimes called triply asymptotic triangles or trebly asymptotic triangles. The vertices are sometimes called ideal vertices. All ideal triangles are congruent.

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Ideal triangle

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In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points. Ideal triangles are also sometimes called...

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Hyperbolic triangle

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A triangle with one ideal vertex is called an omega triangle. Special Triangles with ideal vertices are: A triangle where one vertex is an ideal point...

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Ideal point

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ideal points; two horocycles are concentric when they have the same centre. if all vertices of a triangle are ideal points the triangle is an ideal triangle...

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Ideal

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"negligible" Ideal (Lie algebra), a particular subset in a Lie algebra Ideal point, a boundary point in hyperbolic geometry Ideal triangle, a triangle in hyperbolic...

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Golden ratio

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on one side of an ideal triangle to the closer of the other two sides: this distance, the side length of the equilateral triangle formed by the points...

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Schwarz triangle

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subgroup of the reflection group of the triangle is a Hecke group. For an ideal triangle in which all angles are zero, so that all vertices lie on the real axis...

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Sum of angles of a triangle

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(but positive). For an ideal triangle, a generalization of hyperbolic triangles, this sum is equal to zero. For a spherical triangle, the sum of the angles...

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Schwarz triangle function

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α, but that is not an option for an ideal triangle having all angles zero. Instead, a mapping to an ideal triangle with vertices at 0, 1, and ∞ is given...

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Triangular theory of love

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triangles, according to Acker and Davis and many others, are 'real' triangles, 'ideal' triangles, and 'perceived' triangles. These 'real' triangles are...

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Uniform tilings in hyperbolic plane

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paracompact hyperbolic triangle and creates uniform tilings with either infinite faces (called apeirogons) that converge to a single ideal point, or infinite...

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Hyperbolic geometry

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a hyperbolic ideal triangle in which all three angles are 0° is equal to this maximum. As in Euclidean geometry, each hyperbolic triangle has an incircle...

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Ideal gas law

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The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior...

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Limiting parallel

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coterminal. If, in a hyperbolic triangle, the pairs of sides are limiting parallel, then the triangle is an ideal triangle. A ray A a {\displaystyle Aa}...

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Deltoid curve

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Circular horn triangle, a three-cusped curve formed from circular arcs Ideal triangle, a three-cusped curve formed from hyperbolic lines Pseudotriangle, a...

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Hyperbolic metric space

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geodesic triangle is the circle of largest diameter contained in the triangle and every geodesic triangle lies in the interior of an ideal triangle, all of...

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Arbelos

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Poincaré half-plane model of the hyperbolic plane, an arbelos models an ideal triangle. The name arbelos comes from Greek ἡ ἄρβηλος he árbēlos or ἄρβυλος árbylos...

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Ideal polyhedron

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polyhedron (one with all faces triangles) has all vertex degrees between four and six (inclusive) then it has an ideal representation, but the triakis...

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Hexagon

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Schläfli symbol {6} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined...

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Triangle Fraternity

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Coat of Arms on a Yellow T with Gray field. Triangle Fraternity was founded on high ethical and moral ideals, and expects the men of the fraternity to follow...

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Hyperbolic manifold

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construct the thrice-punctured sphere, shown below, by gluing two ideal triangles together. This also shows how to draw curves on the surface – the black...

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Angle of parallelism

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(a)} is the angle at the non-right angle vertex of a right hyperbolic triangle having two asymptotic parallel sides. The angle depends on the segment...

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Theory of forms

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Form of a triangle. For the form of a triangle say there is a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is...

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Female body shape

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Triangle, Inverted Triangle}", 2002 Connell's "Body Shape Assessment Scale: {Hourglass, Pear, Rectangle, Inverted Triangle}", 2006 Rasband: {Ideal, Triangular...

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Federal Triangle

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Federal Triangle is a triangular area in Washington, D.C. formed by 15th Street NW, Constitution Avenue NW, Pennsylvania Avenue NW, and E Street NW. Federal...

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