Gregory's ServerThe optimal shape is the one already known (due to Gerver), but we didn't know it was the shape with the largest area relative to the size of the hallway.
Here's a picture of it moving around the corner
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 The optimal shape is the one already known (due to Gerver), but we didn't know it was the shape with the largest area relative to the size of the hallway. Here's a picture of it moving around the corner 1 comment
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@highergeometer Now somebody just needs to make a sofa that shape.