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Putnam
1942 Putnam
A6
A6
Part of
1942 Putnam
Problems
(1)
Putnam 1942 A6
Source: Putnam 1942
3/1/2022
Any circle in the
x
y
xy
x
y
-plane is "represented" by a point on the vertical line through the center of the circle and at a distance "above" the plane of the circle equal to the radius of the circle. Show that the locus of the representations of all the circles which cut a fixed circle at a constant angle is a portion of a one-sheeted hyperboloid. By consideration of a suitable family of circles in the plane, demonstrate the existence of two families of rulings on the hyperboloid.
Putnam
Hyperboloid