What Is the Maximum Length of a Bar That Can Fit Through a Corner?

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The discussion revolves around solving the "around the corner" problem, which involves determining the maximum length of a bar that can fit through a corner formed by two intersecting hallways. Participants suggest drawing a diagram to visualize the widths of the hallways, labeled as x and y. The key insight is that the longest bar that can fit through the corner is represented by the diagonal of the rectangle formed by the intersection of the two hallways. This geometric approach helps in calculating the maximum length effectively. Understanding this concept is essential for solving the assignment accurately.
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"Around the corner" problem?

Hey, I got this assignment from my class... it asks for the maximum length for a bar in order to get it through a corner created by 2 hallways... I am provided with the width of the 2 hallways and that's it. Can someone gimme a suggestion?
Thanks

Nam
 
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Draw a diagram of the two hallways, where x and y are the widths of the two hallways.
________________________________________
| |
| |
| x
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| |________________________
|-------y--------|
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I'd think the maximum bar would be the longest line you can draw in the rectangle formed by the intersection of the hallways; ie the diagonal.

PS sorry about the diagram; it looked fine when I was writing it. Move a vertical line over to the right(to the end of the y line) and it really does look like two hallways
 
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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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