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In mathematics, Pappus' centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus' theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. The theorems are attributed to Pappus of Alexandria and Paul Guldin. ==The first theorem== The first theorem states that the surface area ''A'' of a surface of revolution generated by rotating a plane curve ''C'' about an axis external to ''C'' and on the same plane is equal to the product of the arc length ''s'' of ''C'' and the distance ''d'' traveled by its geometric centroid. : For example, the surface area of the torus with minor radius ''r'' and major radius ''R'' is : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pappus's centroid theorem」の詳細全文を読む スポンサード リンク
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