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Putnam
1971 Putnam
B4
B4
Part of
1971 Putnam
Problems
(1)
Putnam 1971 B4
Source:
4/6/2022
A "spherical ellipse" with foci
A
,
B
A,B
A
,
B
on a given sphere is defined as the set of all points
P
P
P
on the sphere such that
P
A
⌢
+
P
B
⌢
=
\overset{\Large\frown}{PA}+\overset{\Large\frown}{PB}=
P
A
⌢
+
PB
⌢
=
constant. Here
P
A
⌢
\overset{\Large\frown}{PA}
P
A
⌢
denotes the shortest distance on the sphere between
P
P
P
and
A
A
A
. Determine the entire class of real spherical ellipses which are circles.
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