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  2. Polygon partition - Wikipedia

    en.wikipedia.org/wiki/Polygon_partition

    The fair polygon partitioning problem [20] is to partition a (convex) polygon into (convex) pieces with an equal perimeter and equal area (this is a special case of fair cake-cutting). Any convex polygon can be easily cut into any number n of convex pieces with an area of exactly 1/n. However, ensuring that the pieces have both equal area and ...

  3. Cutting stock problem - Wikipedia

    en.wikipedia.org/wiki/Cutting_stock_problem

    The presence of length variations creates a 2-D problem, because waste can occur both width-wise and length-wise. [citation needed] The guillotine problem is another 2-D problem of cutting sheets into rectangles of specified sizes, however only cuts that continue all the way across each sheet are allowed. Industrial applications of this problem ...

  4. Array slicing - Wikipedia

    en.wikipedia.org/wiki/Array_slicing

    In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original. Common examples of array slicing are extracting a substring from a string of characters, the " ell " in "h ell o", extracting a row or column from a two ...

  5. Graph partition - Wikipedia

    en.wikipedia.org/wiki/Graph_partition

    Consider a graph G = (V, E), where V denotes the set of n vertices and E the set of edges. For a (k,v) balanced partition problem, the objective is to partition G into k components of at most size v · (n/k), while minimizing the capacity of the edges between separate components. [1]

  6. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.

  7. Pizza theorem - Wikipedia

    en.wikipedia.org/wiki/Pizza_theorem

    Hirschhorn et al. (1999) show that a pizza sliced in the same way as the pizza theorem, into a number n of sectors with equal angles where n is divisible by four, can also be shared equally among n/4 people. For instance, a pizza divided into 12 sectors can be shared equally by three people as well as by two; however, to accommodate all five of ...

  8. Dividing a square into similar rectangles - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_square_into...

    However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...

  9. Piecewise function - Wikipedia

    en.wikipedia.org/wiki/Piecewise_function

    Piecewise functions can be defined using the common functional notation, where the body of the function is an array of functions and associated subdomains. A semicolon or comma may follow the subfunction or subdomain columns. [ 4 ]