Take a look at this figure:
What's the length of the longest 1-dimensional rod which can pass through this corridor horizontally? I can solve this problem mathematically using first and second derivative tests, but is there an easier way, similar to what feynman does in many of his lectures? One approach might be to take advantage of the symmetry of the situation.
The longest such rod will make an angle of pi/4 with the original direction when it (almost) touches the inner corner. I need a valid logical explaination for that.
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