# Equidecomposition of Two Parallelograms

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A Mathematical Droodle

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Copyright © 1996-2018 Alexander BogomolnyThe applet purports to illustrate a simple fact:

Two parallelograms with equal areas and bases are equidecomposable.

This is of course a direct consequence of the Wallace-Bolyai-Gerwien Theorem. However, as the proof goes, the number of pieces that is produced is greatly exaggerated. In particular cases it is always possible to use fewer pieces. The case of two parallelograms above serves to illustrate that point.

### Equidecomposition by Dissiection

- Carpet With a Hole
- Equidecomposition of a Rectangle and a Square
- Equidecomposition of Two Parallelograms
- Equidecomposition of Two Rectangles
- Equidecomposition of a Triangle and a Rectangle
- Equidecomposition of a Triangle and a Rectangle II
- Two Symmetric Triangles Are Directly Equidecomposable
- Wallace-Bolyai-Gerwien Theorem
- Perigal's Proof of the Pythagorean Theorem
- A Proof Perigal and All Others After Him Missed
- Dissection of a Vase
- Curvy Dissection

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny66195967