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The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
E_2={d,e}. d is labeled 3, and has one edge to f. e is labeled 1, and has one edge to f and one to g. E_3={f,g}. f is labeled 4. g is labeled 1. Etc. An ordered Bratteli diagram is a Bratteli diagram together with a partial order on E n such that for any v ∈ V n the set { e ∈ E n−1 : r(e) = v } is totally ordered. Edges that do not share ...
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
Polygon decomposition is applied in several areas: [1] Pattern recognition techniques extract information from an object in order to describe, identify or classify it. An established strategy for recognising a general polygonal object is to decompose it into simpler components, then identify the components and their interrelationships and use this information to determine the shape of the object.
If the corners of one pentagon in P1 are labeled in succession by 1,3,5,2,4 an unambiguous tagging in all the pentagons is established, the order being either clockwise or counterclockwise. Points with the same label define a tiling by Robinson triangles while points with the numbers 3 and 4 on them define the vertices of a Tie-and-Navette tiling.
A rectangle with four equal sides [1] A rhombus with a right angle between a pair of adjacent sides [1] A rhombus with all angles equal [1] A parallelogram with one right angle and two adjacent equal sides [1] A quadrilateral with four equal sides and four right angles; that is, a quadrilateral that is both a rhombus and a rectangle [1]
A separator square in a polygon P is a square s in P such that P−s is not connected. Lemma: in a simple rectilinear polygon, a maximal square that does not contain a knob is a separator. [3] A square containing a knob may or may not be a separator. The number of different separator squares may be infinite and even uncountable. For example, in ...
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.