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  2. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [ 15 ] [ 16 ] de Bruijn's theorem : A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p , q , r (i.e., the box is a multiple of the brick.) [ 15 ]

  3. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density, η, of an ...

  4. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. [8]

  5. Pattern Blocks - Wikipedia

    en.wikipedia.org/wiki/Pattern_blocks

    Pattern Blocks are a set of mathematical manipulatives developed in the 1960s. The six shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things, they allow children to see how shapes can be composed and ...

  6. 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 ⁠.

  7. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of d𝜃 at the centre of the circle), each with an area of ⁠ 1 / 2 ⁠ · r 2 · d𝜃 (derived from the expression for the area of a triangle: ⁠ 1 / 2 ⁠ · a · b · sin𝜃 ...

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