You have an ink stamp that is so amazingly precise that, when inked and pressed down on the plane, it makes every circle whose radius is an irrational number (centered at the center of the stamp) black.
Is it possible to use the stamp three times and make every point in the plane black?
If it is possible, where would you center the three stamps?
(In reply to
re(2): Brian's solution by Cory Taylor)
Cory,
Please reread my post.
The first example I gave is NOT where x is transcendental.
The second example I gave is.
The points (in both examples) I gave ARE colinear, but they're not equidistant (i.e., on a circle) from anything, so I'm not sure what you're talking about.
Again, in my second example, x is indeed transcendental in all three points, and the stamp will not cover the plane.
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If I understand what you wrote, you are saying that as long as the distance between successive points is constant (and transcendental), and they are colinear, then the three stamps will cover the plane.
Without analysis, I'm not certain whether or not that is correct. But, either way, I did not get that notion from what Larry wrote. Larry didn't mention anything about distance between points, so I interpret his 'x' as the horizontal coordinate (standard on the Cartesian plane).
Edited on December 8, 2003, 12:30 pm
re(3): Brian's solution
