Category:Pappus's Theorems

This category contains pages concerning Pappus's Theorems:

There are $2$ theorems which bear the name of Pappus of Alexandria:

Pappus Centroid Theorems, also known as the Pappus-Guldinus Theorems

These comprise the $2$ separate theorems:

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 $S$.

Pappus's Hexagon Theorem

Let $A, B, C$ be a set of collinear points.

Let $a, b, c$ be another set of collinear points.

Let $X, Y, Z$ be the points of intersection of each of the straight lines $Ab$ and $aB$, $Ac$ and $aC$, and $Bc$ and $bC$.

Then $X, Y, Z$ are collinear points.

Source of Name

This entry was named for Pappus of Alexandria.