Second Pappus-Guldinus Theorem

Theorem

Let $C$ be a plane figure that lies entirely on one side of a straight line $L$.

Let $S$ be the solid of revolution generated by $C$ around $L$.

Then the surface area of $S$ is equal to the perimeter length of $C$ multiplied by the distance travelled by the centroid of $C$ around $L$ when generating $S$.


Proof


This theorem requires a proof.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.



Also known as

The is also known as:

Pappus's Centroid Theorem for Surface Area
the Second Guldinus Theorem.


Also see


Source of Name

This entry was named for Pappus of Alexandria and Paul Guldin.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Pappus' theorems (1)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pappus' theorems (1)
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Pappus' Theorems
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.