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Henry Dudeney
A new research has confirmed that Dudeney’s original solution is even the best possible answer to the mathematical problem.
A team of investigators officially confirmed that the centenary solution to the famous Dudeney geometric dissection problem It is the best possible answer.
The new study, led by Professor Ryuhei Uehara and assistant professor Tonan Kamata at the Japan Advanced Institute of Science and Technology (Jaist), proves that an equilateral triangle cannot be cut in less than four parts to form a perfect square. The research was at the Arxiv Open Access Repository and presented at 23rd LA/EATCS-Japan Workshop on Theoretical Computer Science in January 2025.
In 1907, British mathematician Henry Ernest Dudeney proposed a now famous puzzle: what is the minimum number of pieces needed to cut an equilateral triangle and reorganize them in a perfect square? Dudeney’s own solution, revealed a few weeks later, required four pieces. However, despite the elegance of their method, mathematicians debated for more than a century if there could be a solution with fewer pieces.
Erik D. Demaine / Tonan Kamata / Ryuhei Uehara
Original Dudeney problem solution
Geometric dissections like this one that fascinates mathematicians and have practical applications in areas such as textile manufacture, engineering and design. The main challenge is to minimize the number of cuts, while allowing an exact transformation between shapes, explains the.
The investigation proves once and for all that Dudeney’s four -piece solution is great. Using a new mathematical approach called correspondence diagrams, the team systematically excluded the possibility From a two or three -piece dissection and has shown that no three or less part arrangement could successfully turn an equilateral triangle into a square without revealing the pieces – an important restriction on Dudeney’s original solution.
By reducing the problem to a structure based on a graph that captures the relations between edges and vertices in the dissection, the researchers presented a rigorous mathematics. Their findings establish that any attempt to solve Puzzle with less than four pieces is impossible.
This investigation is significant beyond the simple resolution of a centenary puzzle. “The ability to cut and rearrange forms efficiently has been crucial since the beginning of human history, since processing of animal skins to modern industrial applications”Explained Professor Uehara.
The new test technique may revolutionize the study of geometric dissections, leading to optimized solutions to the manufacture, conception and efficiency of materials.
