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In geometry, visibility is a mathematical abstraction of the real-life notion of visibility.. Given a set of obstacles in the Euclidean space, two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles.
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In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
The Cayley graph of a free group with two generators. This is a hyperbolic group whose Gromov boundary is a Cantor set. Hyperbolic groups and their boundaries are important topics in geometric group theory, as are Cayley graphs. The (6,4,2) triangular hyperbolic tiling. The triangle group corresponding to this tiling has a circle as its Gromov ...
1. Boundary of a topological subspace: If S is a subspace of a topological space, then its boundary, denoted , is the set difference between the closure and the interior of S. 2. Partial derivative: see ∂ / ∂ . ∫ 1. Without a subscript, denotes an antiderivative.
The boundary E 3 is therefore the empty set. Indeed, consider a point in the plane, say (x 0,y 0). This point lies on a tangent line if and only if there exists a t such that (, (,)) = = . This is a cubic in t and as such has at least one real solution. It follows that at least one tangent line to γ must pass through any given point in the plane.
Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection. In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit ...
The proof of the Brunn–Minkowski inequality predates modern measure theory; the development of measure theory and Lebesgue integration allowed connections to be made between geometry and analysis, to the extent that in an integral form of the Brunn–Minkowski inequality known as the Prékopa–Leindler inequality the geometry seems almost ...