The pappus guldin theorems suppose that a plane curve is rotated about an axis external to the curve. In mathematics, pappuss centroid theorem also known as the guldinus theorem, pappus guldinus theorem or pappuss theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. Pappus s hexagon theorem theorem that, if the vertices of a hexagon lie alternately on two lines, then the three pairs of opposite sides meet in three collinear points upload media. Files are available under licenses specified on their description page. Pappus s first theorem states that the area of a surface generated by rotating a figure about an external axis a distance from its centroid equals the product of the arc length of the generating figure and the distance traversed by. Pappus s theorem, in mathematics, theorem named for the 4thcentury greek geometer pappus of alexandria that describes the volume of a solid, obtained by revolving a plane region d about a line l not intersecting d, as the product of the area of d and the length of the circular path traversed by the centroid of d during the revolution. Moreover, very little is known of what his actual contributions were or even exactly when he lived. All structured data from the file and property namespaces is available under the creative commons cc0 license. In mathematics, pappuss centroid theorem also known as the guldinus theorem, pappusguldinus theorem or pappuss theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. Century ad proposed two theorems for determining the area and volume of surfaces of revolution. Media in category pappus guldinus theorem the following 6 files are in this category, out of 6 total.
Long before the invention of calculus, pappus of alexandria ca. We do know that he recorded in one of his commentaries on the almagest2 that he observed a solar eclipse on october 18, 320. Geometry articles, theorems, problems, and interactive. The nine points of pappus s theorem are the two triples of points on the initial two lines and the three points of intersection which. Descargue como pdf, txt o lea en linea desde scribd. The nine lines are the two initial lines, the six zigzag lines between the points and.
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