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Word problem for groups. In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group is the algorithmic problem of deciding whether two words in the generators represent the same element of . The word problem is a well-known example of an undecidable problem.
Cuisenaire rods in a staircase arrangement Interlocking "multilink" linking cubes A Polydron icosahedron. In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts ...
The Herzberger Quader, as it was published on the occasion of the 50th anniversary of high school graduation in Herzberg. The Herzberger Quader is a solid dissection puzzle invented by German mathematics teacher Gerhard Schulze. [1] It was named after his home-town Herzberg, and Quader is the latin-derived German word for a rectangular cuboid.
Soma cube. The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 [1] during a lecture on quantum mechanics conducted by Werner Heisenberg. [2] Seven different pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes.
The Rubik's Cube is a 3D combination puzzle invented in 1974 [ 2 ][ 3 ] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, [ 4 ] the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, [ 5 ] and then by Ideal Toy Corp in 1980 [ 6 ] via businessman Tibor Laczi and Seven ...
15 puzzle. To solve the puzzle, the numbers must be rearranged into numerical order from left to right, top to bottom. The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and more) is a sliding puzzle. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with ...
The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2 64 −1 or 18,446,744,073,709,551,615 (eighteen quintillion ...
Cube (algebra) y = x3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The cube is also the number ...
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