Document Type
Poster
Abstract
The Wallace-Bolyai-Gerwien theorem states any polygon can be decomposed into a fnite number of polygonal pieces that can be translated and rotated to form any polygon of equal area. The theorem was proved in the early 19th century. The mini-mum number of pieces necessary to form these common dissections remains an open question. In 1905, Henry Dudney demonstrated a four-piece common dissection be-tween a square and equilateral triangle. We investigate the possible existence of a three-piece common dissection. Specifcally we conjecture that there does not exist a three-piece common dissection using only convex polygons.
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Publication Date
2017
Keywords
Wallace-Bolyai-Gerwien theorem, polygons, three-piece common dissection
Disciplines
Mathematics
Recommended Citation
DeGiovanni, Trent, "The Most Economical Common Dissection of a Square and Equilateral Triangle" (2017). Math Student Scholarship. 1.
https://repository.gonzaga.edu/mathstudentschol/1
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