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  2. Word problem for groups - Wikipedia

    en.wikipedia.org/wiki/Word_problem_for_groups

    For example, polycyclic groups have solvable word problems since the normal form of an arbitrary word in a polycyclic presentation is readily computable; other algorithms for groups may, in suitable circumstances, also solve the word problem, see the Todd–Coxeter algorithm [8] and the Knuth–Bendix completion algorithm. [9]

  3. Word problem (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Word_problem_(mathematics)

    The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]

  4. Word problem (mathematics education) - Wikipedia

    en.wikipedia.org/wiki/Word_problem_(mathematics...

    Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

  5. Division (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Division_(mathematics)

    In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or ⁠ 20 / 5 ⁠ = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...

  6. Word Processing in Groups - Wikipedia

    en.wikipedia.org/wiki/Word_Processing_in_Groups

    Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by the behavior of finite automata. The book's authors are David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston.

  7. Word (group theory) - Wikipedia

    en.wikipedia.org/wiki/Word_(group_theory)

    In group theory, a word is any written product of group elements and their inverses. For example, if x , y and z are elements of a group G , then xy , z −1 xzz and y −1 zxx −1 yz −1 are words in the set { x , y , z }.

  8. 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.

  9. Divide and choose - Wikipedia

    en.wikipedia.org/wiki/Divide_and_choose

    Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource ("the cake") and two partners who have different preferences over parts of the cake (both want as much of it as possible).

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