What is it about?
It can be checked that 1^2 + 2^2 + ... +24^2 = 70^2. We explore a natural extension of this: can the squares 1x1, 2x2,..., 24x24 precisely fit into a 70x70 square?
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Why is it important?
Rectangle packing is an important area of Mathematical research, and is such for the efficiency relating back to real-world constraints. An example of a real-world packing problem is a shipping company has 100 boxes of a variety of sizes, to find the most efficient way of stacking/ arranging the boxes is a packing problem.
Perspectives
This particular problem has been researched before but it is our hope that our paper provides new methods in approaching this problem. The most commonly seen method of this problem is (entirely) computer-based, and our method is more construction-based. We hope to inspire new methods of approaching this problem/ new ways of thinking about this problem.
Brian Laverty
West Virginia University
Read the Original
This page is a summary of: Optimal Rectangle Packing for the 70 Square, Recreational Mathematics Magazine, September 2018, De Gruyter,
DOI: 10.2478/rmm-2018-0001.
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