Wallace-Bolyai-Gerwien Theorem

Theorem

Let $A$ and $B$ be plane rectilinear figures.

Then:

there exists a dissection of $A$ into components which can be reassembled to form $B$

if and only if:

$A$ 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