# Wallace-Bolyai-Gerwien Theorem

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## 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

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## 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**