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  2. Sierpiński carpet - Wikipedia

    en.wikipedia.org/wiki/Sierpiński_carpet

    But, if this square has not been previously removed, it must have been holed in iteration k + 1, so it cannot be contained in the carpet – a contradiction. The Hausdorff dimension of the carpet is log ⁡ 8 log ⁡ 3 ≈ 1.8928 {\displaystyle {\frac {\log 8}{\log 3}}\approx 1.8928} .

  3. Area formulas - Wikipedia

    en.wikipedia.org/wiki/Area

    1 square yard = 9 square feet; 1 square mile = 3,097,600 square yards = 27,878,400 square feet; In addition, conversion factors include: 1 square inch = 6.4516 square centimetres; 1 square foot = 0.092 903 04 square metres; 1 square yard = 0.836 127 36 square metres; 1 square mile = 2.589 988 110 336 square kilometres

  4. Square yard - Wikipedia

    en.wikipedia.org/wiki/Square_yard

    Comparison of 1 square yard with some Imperial and metric units of area The square yard ( Northern India : gaj , Pakistan : gaz ) is an imperial unit and U.S. customary unit of area . It is in widespread use in most of the English -speaking world, particularly the United States, United Kingdom, Canada, Pakistan and India.

  5. Sierpiński curve - Wikipedia

    en.wikipedia.org/wiki/Sierpiński_curve

    A space-filling curve is a continuous map of the unit interval onto a unit square and so a (pseudo) inverse maps the unit square to the unit interval. One way of constructing a pseudo-inverse is as follows. Let the lower-left corner (0, 0) of the unit square correspond to 0.0 (and 1.0).

  6. Menger sponge - Wikipedia

    en.wikipedia.org/wiki/Menger_sponge

    Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry. [8]

  7. Knot density - Wikipedia

    en.wikipedia.org/wiki/Knot_density

    For two carpets of the same age, origin, condition and design, the one with the higher number of knots will be the more valuable. Knot density is normally measured in knots per square inch (KPSI) which is simply the number of vertical knots across one inch of carpet multiplied by the number of horizontal knots in the same area. Average knot ...

  8. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

  9. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...

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