Semicircle
Translation- Semicircle
In
mathematics (more specificallygeometry ), a semicircle is a two-dimensionalgeometric shape that formshalf of acircle . Being half of a circle's 360°, the arc of a semicircle always measures 180°. A triangle inscribed in a semicircle is always aright triangle .Uses
A semicircle can be used to construct arithmetic and geometric means of two lengths using straight-edge and compass. If we make a semicircle with a diameter of "a"+"b", then the length its radius is the arithmetic mean (since it's half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths "a" and "b", and then connecting their common end and the semicircle with a segment perpendicular to the diameter. The length of the resulting segment is the geometric mean [Euclid's Elements, Book VI, Proposition 13 [http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI13.html] ] , which can be proved using
Pythagorean theorem .This method can be used to accomplish quadrature of a rectangle (since a square whose sides are equal to geometric mean of sides of a rectangle has the same
area as the rectangle), and thus any figure for which we can construct a rectangle with equal area, such as anypolygon (but not a circle).References
ee also
*
Thales' theorem External links
* [http://mathworld.wolfram.com/Semicircle.html Semicircle - Mathworld]
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semicircle — noun полукруг … Англо-русский словарь Мюллера
Semicircle — Sem i*cir cle, n. 1. (a) The half of a circle; the part of a circle bounded by its diameter and half of its circumference. (b) A semicircumference. [1913 Webster] 2. A body in the form of half of a circle, or half of a circumference. [1913… … The Collaborative International Dictionary of English
semicircle — 1> полукруг, полуокружность … Новый большой англо-русский словарь
semicircle — ˈsemɪˌsə:kl сущ. полукруг; полукруглая структура, форма; полукруглый инструмент полукруг, полуокружность semicircle полукруг … Большой англо-русский и русско-английский словарь
semicircle — noun Etymology: Latin semicirculus, from semi + circulus circle Date: 1526 1. a half of a circle 2. an object or arrangement of objects in the form of a half circle • semicircular adjective … New Collegiate Dictionary
semicircle — полукруг … Англо-русский словарь технических терминов
semicircle — semicircular /sem i serr kyeuh leuhr/, adj. semicircularly, adv. semicircularness, n. /sem i serr keuhl/, n. 1. Also called semicircumference /sem ee seuhr kum feuhr euhns, freuhns, sem uy /. half of a circle; the arc from one end of a diameter… … Universalium
semicircle — 1) полукруг 2) полуокружность … Англо-русский технический словарь
semicircle — noun Half of a circle … Wiktionary
Wigner semicircle distribution — Probability distribution name =Wigner semicircle type =density pdf | cdf parameters =R>0! radius (real) support =x in [ R;+R] ! pdf =frac2{pi R^2},sqrt{R^2 x^2}! cdf =frac12+frac{xsqrt{R^2 x^2{pi R^2} + frac{arcsin!left(frac{x}{R} ight)}{pi}! for … Wikipedia