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2. Penrose tiling - Wikipedia

   en.wikipedia.org/wiki/Penrose_tiling

   Penrose tiling. A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both ...

3. Aperiodic tiling - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_tiling

   An aperiodic tiling using a single shape and its reflection, discovered by David Smith. An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non- periodic tilings.

4. Wheat and chessboard problem - Wikipedia

   en.wikipedia.org/wiki/Wheat_and_chessboard_problem

   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 ...

5. Euclidean tilings by convex regular polygons - Wikipedia

   en.wikipedia.org/wiki/Euclidean_tilings_by...

   Euclidean tilings are usually named after Cundy & Rollett’s notation. [ 1] This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6; 3 6; 3 4 .6, tells us there are 3 vertices with 2 different vertex types ...

6. Cuisenaire rods - Wikipedia

   en.wikipedia.org/wiki/Cuisenaire_rods

   Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on [ 1] way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. [ 2][ 3] In the early 1950s, Caleb Gattegno popularised this set of coloured number rods ...

7. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...