Wallace-Bolyai-Gerwien Theorem
(Redirected from Bolyai-Gerwien Theorem)
Jump to navigation
Jump to search
Theorem
Let $A$ and $B$ be plane rectilinear figures.
Then:
- there exists a dissection of $A$ into components which can be reassembled to form $B$
- $A$ and $B$ have the same area.
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 Wallace-Bolyai-Gerwien Theorem is also known as the Bolyai-Gerwien Theorem.
Source of Name
This entry was named for William Wallace, Farkas Wolfgang Bolyai and Karl Ludwig Gerwien.
Historical Note
William Wallace first formulated the theorem which would later be called the Wallace-Bolyai-Gerwien Theorem in $1807$.
Farkas Wolfgang Bolyai and Karl Ludwig Gerwien independently proved the same thing in $1833$ and $1835$ respectively.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dissection proof