Semicircle

Semicircle

In mathematics (more specifically geometry), a semicircle is a two-dimensional geometric shape that forms half of a circle. Being half of a circle's 360°, the arc of a semicircle always measures 180°. A triangle inscribed in a semicircle is always a right 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 any polygon (but not a circle).

References

ee also

*Thales' theorem

External links

* [http://mathworld.wolfram.com/Semicircle.html Semicircle - Mathworld]


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  • 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 — 1520s, from SEMI (Cf. semi ) + CIRCLE (Cf. circle). Semicircular is attested from early 15c …   Etymology dictionary

  • semicircle — ► NOUN ▪ a half of a circle or of its circumference. DERIVATIVES semicircular adjective …   English terms dictionary

  • semicircle — [sem′i sʉr΄kəl] n. [L semicirculus: see SEMI & CIRCLE] 1. a half circle 2. anything in the form of a half circle semicircular [sem′i sʉr΄kyə lər] adj …   English World dictionary

  • semicircle — n. 1) to form a semicircle 2) in a semicircle * * * [ semɪˌsɜːk(ə)l] in a semicircle to form a semicircle …   Combinatory dictionary

  • semicircle — UK [ˈsemɪˌsɜː(r)k(ə)l] / US [ˈsemɪˌsɜrk(ə)l] noun [countable] Word forms semicircle : singular semicircle plural semicircles 1) maths half of a circle 2) a group of people or things arranged in a curved line as if they were around the edge of… …   English dictionary

  • semicircle — sem|i|cir|cle [ˈsemiˌsə:kəl US ə:r ] n half a circle in a semicircle ▪ About 50 children sat in a semicircle around me. >semicircular [ˌsemiˈsə:kjulə US ˈsə:rkjulər] adj …   Dictionary of contemporary English

  • semicircle — sem|i|cir|cle [ semi,sɜrkl ] noun count 1. ) half of a circle 2. ) a group of people or things arranged in a curved line as if they were around the edge of half a circle: The kids sat in a semicircle around the teacher …   Usage of the words and phrases in modern English

  • semicircle — noun (C) 1 half a circle 2 a group arranged in a curved line, as if on the edge of half a circle: Get the kids to sit in a semicircle. semicircular /semi s:kjl/ adjective …   Longman dictionary of contemporary English

  • semicircle — n. 1 half of a circle or of its circumference. 2 a set of objects ranged in, or an object forming, a semicircle. Etymology: L semicirculus (as SEMI , CIRCLE) …   Useful english dictionary

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