PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
Pappus's centroid theorem (Theorem)
GuldinsRule

"Pappus's centroid theorem" is owned by stevecheng.
(view preamble | get metadata)

View style:

See Also: centroid, centre of mass, surface of revolution, volume of solid of revolution

Other names:  Guldin's rule, Guldinus theorem, Guldin's theorem, Pappus's theorem for solids of revolution, Pappus's theorem for surfaces of revolution
Log in to rate this entry.
(view current ratings)

Cross-references: arc, sphere, component, symmetry, plane, ball, parameters, solid, obvious, centre, ring, radius, circle, generating, torus, Pappus's theorems, theorems, area, volume, region, solid of revolution, density, line, centre of mass, rotation, centroid, distance, arc length, surface area, axis, curve, smooth, generated by, surface of revolution

This is version 4 of Pappus's centroid theorem, born on 2005-08-15, modified 2005-08-27.
Object id is 7321, canonical name is PappussTheoremForSurfacesOfRevolution.
Accessed 14856 times total.

Classification:
AMS MSC53A05 (Differential geometry :: Classical differential geometry :: Surfaces in Euclidean space)

Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy
More general hypotheses by stevecheng on 2005-08-27 18:26:07
I'm pretty sure that theorem 1 of the present entry
should work also for rectifiable curves, not merely smooth curves[*];
however I don't know about geometric measure theory in order to prove it.
Can anyone confirm if my conjecture is correct?

[*] N.B. Theorem 2 already allows arbitrary Lebesgue-measurable regions;
this is not hard to prove with the classic measure theory tools.

// Steve
[ reply | up ]

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)