The topic came from a puzzle that was originally posted on Mathstodon stating that a square can be divided into three rectangles with the same proportions. They were able to divide a square into three equal rectangles, a square into rectangles that are 1.5 times as long as they are wide, and the last where they are 1.75847 times as long as wide. The author posed the question of what would the proportions of the rectangles if a square is cut into four rectangles.
Another mathematician sketched out how to find the solution but didn't have the time to actually do it so others did. In fact, people came up with 11 ways that a square could be divided into 4 rectangles with similar proportions. Some of the people created pictures to illustrate the 11 solutions so people could see them rather than trying to visualize them from a description.
The student, Ms Taams, who is using the idea for her Phd at one point posted an 11 part thread explaining the math behind each solution. She also took time to show how this problem is connected to certain formal math. In plain English, her solution showed how the ratios are connected to algebraic numbers which is a major topic in Number Theory.
One person discovered you can use electrical circuit theory to help solve this if you think of the width and height as voltage and current. This way you can "square the square". Furthermore, it lead to people wondering about cutting a square into 5 or 6 rectangles of similar proportion. Upon further inspection, people came up with 51 solutions for 5 similar rectangles in a square and 245 possible solutions for 6 similar rectangles in a square. The number of possibilities jumped to 1,371 solutions for seven rectangles but they are still working on eight rectangles.
So now you know more about the topic of finding the number similar rectangles cut from a square. Let me know what you think, I'd love to hear it. Have a great weekend.
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