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That is, if MWT(i,j) denotes the weight of the minimum-weight triangulation of the polygon below edge ij, then the overall algorithm performs the following steps: For each possible value of i, from n − 1 down to 1, do: For each possible value of j, from i + 1 to n, do: If ij is an edge of the polygon, set MWT(i,j) = length(ij)
The edge-connectivity version of Menger's theorem is as follows: . Let G be a finite undirected graph and x and y two distinct vertices. Then the size of the minimum edge cut for x and y (the minimum number of edges whose removal disconnects x and y) is equal to the maximum number of pairwise edge-disjoint paths from x to y.
The number of sheets in a ream has varied locally over the centuries, often according to the size and type of paper being sold. Reams of 500 sheets (20 quires of 25 sheets) were known in England in c. 1594; [ 15 ] in 1706 a ream was defined as 20 quires, either 24 or 25 sheets to the quire. [ 16 ]
The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence. When a circle is cut n times to produce the maximum number of pieces, represented as p = f (n), the n th cut must be considered; the number of pieces before the last cut is f (n − 1), while the number of pieces added by the last cut is n.
The same set of points can often be constructed using a smaller set of tools. For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already ...
Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2. For unit edge length, R must be halved, giving R = √ 8φ+7 / 2 = √ 11+4 √ 5 / 2 ≈ 2.233.
In the mathematical field of graph theory, the intersection number of a graph = (,) is the smallest number of elements in a representation of as an intersection graph of finite sets. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element.
is the minimum number of edges that need to be cut in order to split the graph in two. The edge expansion normalizes this concept by dividing with smallest number of vertices among the two parts. To see how the normalization can drastically change the value, consider the following example.