Teorema pappus guldin pdf

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. The theorems are attributed to pappus of alexandria and paul guldin. In the situation with zero slope both lines are parallel and the intersection point vanishes. Nine proofs and three variations x y z a b c a b z y c x b a z x c y fig.

Nothing is known of his life, other than what can be found in his own writings. 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. The pappus guldin theorems suppose that a plane curve is rotated about an axis external to the curve. Moreover, very little is known of what his actual contributions were or even exactly when he lived. We do know that he recorded in one of his commentaries on the almagest2 that he observed a solar eclipse on october 18, 320. Consider the curve c given by the graph of the function f. During the development of the paper and at the proposed activities, we used the free software geogebra. Onde s o comprimento da curva geratriz e d a distncia percorrida pelo centride dessa curva em uma rotao completa. Areas of surfaces of revolution, pappuss theorems let f. Guldin published his rediscovered version of pappuss results in 1641.

We, however, claiming as we do a greater share in wis. 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. All structured data from the file and property namespaces is available under the creative commons cc0 license. The hutchinson dictionary of scientific biography helicon publishing, 2004 pappus of alexandria lived c. Files are available under licenses specified on their description page. Let s be the surface generated by revolving this curve about the xaxis. 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. The pappusguldin theorems suppose that a plane curve is rotated about an axis external to the curve. Ad 200350 greek mathematician, astronomer, and geographer whose chief importance lies in his commentaries on the mathematical work of his predecessors. Descargue como pdf, txt o lea en linea desde scribd. This page was last edited on 6 february 2019, at 10. O rcontinua sendo a distancia do centroide da figura ate o eixo em torno do qual a figura gira.