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  2. Involute - Wikipedia

    en.wikipedia.org/wiki/Involute

    In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.

  3. Goat grazing problem - Wikipedia

    en.wikipedia.org/wiki/Goat_grazing_problem

    Find the area between a circle and its involute over an angle of 2 π to −2 π excluding any overlap. In Cartesian coordinates, the equation of the involute is transcendental; doing a line integral there is hardly feasible. A more felicitous approach is to use polar coordinates (z,θ).

  4. 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]

  5. Archimedean spiral - Wikipedia

    en.wikipedia.org/wiki/Archimedean_spiral

    A physical approach is used below to understand the notion of Archimedean spirals.. Suppose a point object moves in the Cartesian system with a constant velocity v directed parallel to the x-axis, with respect to the xy-plane.

  6. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities

  7. Cephalic index - Wikipedia

    en.wikipedia.org/wiki/Cephalic_index

    Cephalic index viewed from above the head. The cephalic index or cranial index is a number obtained by taking the maximum width (biparietal diameter or BPD, side to side) of the head of an organism, multiplying it by 100 and then dividing it by their maximum length (occipitofrontal diameter or OFD, front to back). The index was once used to ...

  8. List of gear nomenclature - Wikipedia

    en.wikipedia.org/wiki/List_of_gear_nomenclature

    Form diameter is the diameter of a circle at which the trochoid (fillet curve) produced by the tooling intersects, or joins, the involute or specified profile. Although these terms are not preferred, it is also known as the true involute form diameter (TIF), start of involute diameter (SOI), or when undercut exists, as the undercut diameter.

  9. Backlash (engineering) - Wikipedia

    en.wikipedia.org/wiki/Backlash_(engineering)

    In mechanical engineering, backlash, sometimes called lash, play, or slop, is a clearance or lost motion in a mechanism caused by gaps between the parts. It can be defined as "the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence."