Pappus-Guldinus Theorems
Theorem
There are two theorems that bear the name Pappus-Guldinus Theorem:
First Pappus-Guldinus Theorem
Let $C$ be a plane figure that lies entirely on one side of a straight line $\LL$.
Let $S$ be the solid of revolution generated by $C$ around $\LL$.
Then the volume of $S$ is equal to the area of $C$ multiplied by the distance travelled by the centroid of $C$ around $\LL$ when generating $S$.
Second Pappus-Guldinus 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 $S$.
Also known as
These theorems are also known as:
Also see
Source of Name
This entry was named for Pappus of Alexandria and Paul Guldin.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.8$: Pappus (fourth century A.D.)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Pappus' Theorems