How Do You Bisect an L-Shaped Figure into Equal Areas?

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The discussion revolves around the challenge of bisecting an L-shaped figure, defined as a larger rectangle with a smaller rectangle cut out from one corner. Participants explore various methods to find a line that divides the area into two equal parts, with some suggesting that multiple bisectors can exist depending on the configuration of the rectangles. A key point is that any line through the centers of the rectangles will bisect both shapes, thus bisecting the L shape. The conversation also touches on the concept of constructibility, noting that certain angles, like 20 degrees, cannot be constructed using a straightedge and compass, which complicates finding a bisector through arbitrary points. Ultimately, the consensus is that while there are infinitely many lines that can bisect the figure, the method of using rectangle centers remains a reliable constructible solution.
  • #31
I wonder if it would not be easier to simply write down equations defining the bisector in terms of the various parameters, and see if it's solvable with square roots.
 
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  • #32
Hurkyl said:
I wonder if it would not be easier to simply write down equations defining the bisector in terms of the various parameters, and see if it's solvable with square roots.

Probably, but I hadn't thought of doing that.
 

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