Teorema pappus guldin pdf

The pappusguldin theorems suppose that a plane curve is rotated about an axis external to the curve. The theorems are attributed to pappus of alexandria and paul guldin. This page was last edited on 6 february 2019, at 10. We do know that he recorded in one of his commentaries on the almagest2 that he observed a solar eclipse on october 18, 320. Files are available under licenses specified on their description page.

During the development of the paper and at the proposed activities, we used the free software geogebra. 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. Ad 200350 greek mathematician, astronomer, and geographer whose chief importance lies in his commentaries on the mathematical work of his predecessors. Nothing is known of his life, other than what can be found in his own writings. O rcontinua sendo a distancia do centroide da figura ate o eixo em torno do qual a figura gira. Nine proofs and three variations x y z a b c a b z y c x b a z x c y fig. Nine proofs and three variations bees, then, know just this fact which is of service to themselves, that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material used in constructing the di. Areas of surfaces of revolution, pappuss theorems let f. Pappusguldinova pravila poznata jos kao guldinova pravila i pappusova pravila, predstavljaju matematicka pravila koja omogucuju jednostavno racunanje nekih rotacijskih povrsina oplosja i volumena obujma pomocu putanje tezista linija likova cijom su rotacijom nastali. Pappuss theorem has been generalized to the case in which the region is allowed to move along any sufficiently smooth no corners, simple no self intersection, closed curve. Moreover, very little is known of what his actual contributions were or even exactly when he lived. Descargue como pdf, txt o lea en linea desde scribd. Guldin published his rediscovered version of pappuss results in 1641.

Consider the curve c given by the graph of the function f. Let s be the surface generated by revolving this curve about the xaxis. The hutchinson dictionary of scientific biography helicon publishing, 2004 pappus of alexandria lived c. In the situation with zero slope both lines are parallel and the intersection point vanishes. The pappus guldin theorems suppose that a plane curve is rotated about an axis external to the curve. All structured data from the file and property namespaces is available under the creative commons cc0 license. We, however, claiming as we do a greater share in wis. Onde s o comprimento da curva geratriz e d a distncia percorrida pelo centride dessa curva em uma rotao completa.