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  2. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: [1] [2] A = s 2 (square). The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes ...

  3. Klee's measure problem - Wikipedia

    en.wikipedia.org/wiki/Klee's_measure_problem

    In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of (multidimensional) rectangular ranges can be computed. Here, a d -dimensional rectangular range is defined to be a Cartesian product of d intervals of real numbers , which is a subset of R d .

  4. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    The area of a rectangle is equal to the product of two adjacent sides. ... Some well-known examples are (3, 4, 5) and (5, 12 ... but the problem does not mention a ...

  5. Rectangle - Wikipedia

    en.wikipedia.org/wiki/Rectangle

    A rectangle is a rectilinear polygon: its sides meet at right angles. A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation), one for shape (aspect ratio), and one for overall size (area).

  6. Quadrature (geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadrature_(geometry)

    A similar geometrical construction solves the problems of quadrature of a parallelogram and of a triangle. Archimedes proved that the area of a parabolic segment is 4/3 the area of an inscribed triangle. Problems of quadrature for curvilinear figures are much more difficult.

  7. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    By Cavalieri's principle, the circle therefore has the same area as that region. Consider the rectangle bounding a single cycloid arch. From the definition of a cycloid, it has width 2πr and height 2r, so its area is four times the area of the circle. Calculate the area within this rectangle that lies above the cycloid arch by bisecting the ...

  8. Largest empty rectangle - Wikipedia

    en.wikipedia.org/wiki/Largest_empty_rectangle

    In computational geometry, the largest empty rectangle problem, [2] maximal empty rectangle problem [3] or maximum empty rectangle problem, [4] is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic ...

  9. Geometric mean theorem - Wikipedia

    en.wikipedia.org/wiki/Geometric_mean_theorem

    area of grey square = area of grey rectangle: = = In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.