Polygon - takakukei (English spelling) polygon

Japanese: 多角形 - たかくけい（英語表記）polygon

A figure bounded by a closed simple broken line consisting of three or more distinct finite points on a plane and line segments (→ straight lines) connecting them. A closed simple broken line is one in which two distinct line segments have only one common part at their end points, and for each point, there are two line segments with that point as one of their end points. The finite number of points are called the vertices of a polygon, and the line segments connecting them are called the sides of the polygon. A polygon with n sides is called an n -gon. The interior angle at a vertex of a polygon is the angle that is inside the polygon, of the two sides whose end points are at that vertex. A polygon with all interior angles less than 180° is called a convex polygon. A polygon with all sides of equal length and all interior angles equal is called a regular polygon, and such an n- gon is called a regular n- gon. In general, the sum of the interior angles of an n -gon is ( n - 2) × 180°. The angle formed by one side of a polygon and the extension of the adjacent side is called the exterior angle, and the sum of the exterior angles of any polygon is 360°. In the field of computer graphics, shapes are approximated by dividing them into polygons, which are often called polygons.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

平面上の相異なる 3個以上の有限個の点と，それらを結ぶ線分（→直線）からなる，閉じた単純折れ線で囲まれた図形。ここで閉じた単純折れ線とは，異なる二つの線分が共通部分をもつとき，それは線分の端点のみであり，またどの点に対しても，それを端点の一つとする線分が 2本存在するものである。有限個の点を多角形の頂点，それらを結ぶ線分を多角形の辺と呼ぶ。n 本の辺をもつ多角形を n角形と呼ぶ。多角形のある頂点における内角とは，その頂点を端点とする 2辺がつくる角のうち多角形の内部にある方をいう。すべての内角が 180°よりも小さい多角形を凸多角形と呼ぶ。すべての辺の長さが等しく，またすべての内角が等しい多角形を正多角形と呼び，そのような n角形を正n角形と表す。一般に，n角形の内角の和は（n－2）×180°である。また，多角形の一辺とその隣の辺の延長がつくる角を外角と呼び，外角の和はどの多角形でも 360°である。コンピュータ・グラフィックスの分野では，図形を多角形に分割して近似することがなされており，これはポリゴンと称されることが多い。

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