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  2. Recreational mathematics - Wikipedia

    en.wikipedia.org/wiki/Recreational_mathematics

    Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.

  3. Cannonball problem - Wikipedia

    en.wikipedia.org/wiki/Cannonball_problem

    A square pyramid of cannonballs in a square frame. In the mathematics of figurate numbers, the cannonball problem asks which numbers are both square and square pyramidal.The problem can be stated as: given a square arrangement of cannonballs, for what size squares can these cannonballs also be arranged into a square pyramid.

  4. Close-packing of equal spheres - Wikipedia

    en.wikipedia.org/wiki/Close-packing_of_equal_spheres

    Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is π 3 2 ≈ 0.74048 {\displaystyle {\frac {\pi }{3{\sqrt {2}}}}\approx 0.74048} .

  5. Ball (mathematics) - Wikipedia

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

    A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a ...

  6. Tangle (mathematics) - Wikipedia

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

    The fraction given by (0,0) is defined as . Conway proved that the fraction is well-defined and completely determines the rational tangle up to tangle equivalence. [1] An accessible proof of this fact is given in:. [2] Conway also defined a fraction of an arbitrary tangle by using the Alexander polynomial.

  7. Elementary mathematics - Wikipedia

    en.wikipedia.org/wiki/Elementary_mathematics

    Rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. [9] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold).

  8. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a/b or ⁠ ⁠, where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include ⁠ 1 / 2 ⁠, − ⁠ 8 / 5 ⁠, ⁠ −8 / 5 ⁠, and ⁠ 8 / −5 ⁠

  9. Block and tackle - Wikipedia

    en.wikipedia.org/wiki/Block_and_tackle

    A block and tackle [1] [2] or only tackle [3] is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift heavy loads.. The pulleys are assembled to form blocks and then blocks are paired so that one is fixed and one moves with the load.