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  2. Ailles rectangle - Wikipedia

    en.wikipedia.org/wiki/Ailles_rectangle

    The Ailles rectangle. The Ailles rectangle is a rectangle constructed from four right-angled triangles which is commonly used in geometry classes to find the values of trigonometric functions of 15° and 75°. [1] It is named after Douglas S. Ailles who was a high school teacher at Kipling Collegiate Institute in Toronto. [2] [3]

  3. Largest empty rectangle - Wikipedia

    en.wikipedia.org/wiki/Largest_empty_rectangle

    E shows a maximal empty rectangle with arbitrary orientation. 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 ...

  4. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]

  5. Surface area - Wikipedia

    en.wikipedia.org/wiki/Surface_area

    A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...

  6. 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).

  7. Rectilinear polygon - Wikipedia

    en.wikipedia.org/wiki/Rectilinear_polygon

    The simplest rectilinear polygon is an axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle . A golygon is a rectilinear polygon whose side lengths in sequence are consecutive integers.

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