Solution
Problem 1189 was solved by Franz Pichler, Joseph DeVincentis, and John
Guilford. Here is a composite solution by Guilford and me.
Observe that in the limiting case that the glass tilts a lot; the water level definitely falls. But for a small tilt angle, the water level rises:
The first image in the array shows a cross-section of the water: the cutting plane is perpendicular to the rotation axis through point P. The second image shows the result of the rotation, imagining the water to be frozen. Point C1 is the rotation of C around P, and is clearly higher. Now, the horizontal plane through C1 (green line in third image) has the same amount of water above it as air space below it, and hence this plane becomes the new upper surface of the water (fourth image). Hence, the water rises.
[Back to Problem 1189]
© Copyright 2014 Stan Wagon. Reproduced with permission.