Equidecomposition of a Rectangle and a Square:
What is this about?
A Mathematical Droodle

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Explanation

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Since every triangle is equidecomposable with a rectangle, we can also claim that every triangle is equidecomposable with a square! An even more obvious conclusion is that two rectangles of equal area are equidecomposable. This fact can be established directly and likely in a more economical manner.

(The problem of constructing a square equal in area to a given rectangle has been solved by Euclid's Elements II.14.)

References

1. G. Frederickson, Dissections: Plane & Fancy, Cambridge University Press, 1997, p. 222

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
  • Two Symmetric Triangles Are Directly Equidecomposable II
  • Two Symmetric Triangles Are Directly Equidecomposable III
  • Two Symmetric Triangles Are Directly Equidecomposable IV
• 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

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