Pappus's centroid theorem

The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.

In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's 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[a] and Paul Guldin.[b] Pappus's statement of this theorem appears in print for the first time in 1659, but it was known before, by Kepler in 1615 and by Guldin in 1640.[4]

  1. ^ Pappus of Alexandria (1986) [c. 320]. Jones, Alexander (ed.). Book 7 of the Collection. Sources in the History of Mathematics and Physical Sciences. Vol. 8. New York: Springer-Verlag. doi:10.1007/978-1-4612-4908-5. ISBN 978-1-4612-4908-5.
  2. ^ Guldin, Paul (1640). De centro gravitatis trium specierum quanitatis continuae. Vol. 2. Vienna: Gelbhaar, Cosmerovius. p. 147. Retrieved 2016-08-04.
  3. ^ Radelet-de Grave, Patricia (2015-05-19). "Kepler, Cavalieri, Guldin. Polemics with the departed". In Jullien, Vincent (ed.). Seventeenth-Century Indivisibles Revisited. Science Networks. Historical Studies. Vol. 49. Basel: Birkhäuser. p. 68. doi:10.1007/978-3-319-00131-9. hdl:2117/28047. ISBN 978-3-3190-0131-9. ISSN 1421-6329. Retrieved 2016-08-04.
  4. ^ Bulmer-Thomas, Ivor (1984). "Guldin's Theorem--Or Pappus's?". Isis. 75 (2): 348–352. ISSN 0021-1753.


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