Rotating body - Rotating body

Japanese: 回転体 - かいてんたい

The locus of a figure F in a plane when it is rotated once around a straight line l in the plane is called a solid of revolution, and l is called the axis of revolution. In particular, when F is a curve, the solid of revolution is called a surface of revolution, and F is called a generating line ( Figure A ). In this case, any position of F during rotation may be called a meridian. The surface of a solid of revolution is a surface of revolution. When F is a figure bounded by the curve y = f(x), two straight lines x = a, x = b, and the x-axis, the volume V of the solid of revolution around the x-axis is a definite integral

( Figure B ).

[Ryoichi Takagi]

Rotating body (Figure A)
©Shogakukan ">

Rotating body (Figure A)

Volume of a rotating body (Figure B)
©Shogakukan ">

Volume of a rotating body (Figure B)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

平面内の図形Fをこの平面内の直線lの周りに1回転させたときのFの軌跡を回転体といい、lを回転軸という。とくにFが曲線のとき、回転体を回転面といい、Fを母線(ぼせん)という（図A）。このとき、回転中のFの任意の位置を子午線ということもある。回転体の表面は回転面である。Fが曲線y＝f(x)と2直線x＝a、x＝bとx軸によって囲まれる図形のとき、x軸の周りの回転体の体積Vは定積分

で与えられる（図B）。

［高木亮一］

回転体〔図A〕
©Shogakukan">

回転体〔図A〕

回転体の体積〔図B〕

出典　小学館　日本大百科全書(ニッポニカ)日本大百科全書(ニッポニカ)について　情報 | 凡例

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