Wallace-Bolyai-Gerwien Theorem

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


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.


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 WallaceFarkas 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.