Search results
Results From The WOW.Com Content Network
To convert a graph with a unique triangle per edge into a triple system, let the triples be the triangles of the graph. No six points can include three triangles without either two of the three triangles sharing an edge or all three triangles forming a fourth triangle that shares an edge with each of them.
A circular triangle is a triangle with circular arc edges. The edges of a circular triangle may be either convex (bending outward) or concave (bending inward). [c] The intersection of three disks forms a circular triangle whose sides are all convex. An example of a circular triangle with three convex edges is a Reuleaux triangle, which can be made
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
Each pair of triangles gives a path of length three that includes the edge connecting the triangles together with two of the four remaining triangle edges. [3] By applying Petersen's theorem to the dual graph of a triangle mesh and connecting pairs of triangles that are not matched, one can decompose the mesh into cyclic strips of triangles.
The original motivation for the study of triangle removal lemma was the Ruzsa–Szemerédi problem.Its initial formulation due to Imre Z. Ruzsa and Szemerédi from 1978 was slightly weaker than the triangle removal lemma used nowadays and can be roughly stated as follows: every locally linear graph on vertices contains () edges. [6]
The intersection of three circular disks forms a convex circular triangle. For instance, a Reuleaux triangle is a special case of this construction where the three disks are centered on the vertices of an equilateral triangle, with radius equal to the side length of the triangle. However, not every convex circular triangle is formed as an ...
Removing a triangle of this type produces a polygon with fewer sides, and repeatedly removing ears allows any simple polygon to be triangulated. Conversely, if a polygon is triangulated, the weak dual of the triangulation (a graph with one vertex per triangle and one edge per pair of adjacent triangles) will be a tree and each leaf of the tree ...
The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2] If the prism's edges are perpendicular to the base, the lateral faces are rectangles, and the prism is called a right triangular prism. [3]