I’d really appreciate if you can help me out with the following question:

Nick bought a table for his basement. Unfortunately, he discovered that his table rocked back and forth on its four legs. After measuring the table legs and finding that they were all exactly the same length, he decided his problem was that the basement concrete floor was uneven. Assuming the surface of the floor is continuous, show that if Nick rotates the table it will stabilize in less than a 90 degree turn.

Thank you for your time.

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