Borsuk-Ulam Theorem
The Borsuk-Ulam Theorem states that any continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. (Two points on a sphere are called antipodal if they sit on directly opposite sides of the sphere's center.)The case n = 2 is often illustrated by saying that at any moment there is always a pair of antipodal points on the Earth's surface with equal temperature and equal barometric pressure. This assumes that temperature and barometric pressure vary continuously.
The Borsuk-Ulam Theorem was first conjectured by Stanislaw Ulam. It was proved by Karol Borsuk[?] in 1933.
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taken place between us.
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Worthington, who had chased me as far as Hancock and had there lost
they might have looked elsewhere for me; but while I was
came an officer from Worthington with a warrant for my arrest. This
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into the worst possible hands.
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accompanied him were willing to swear my life away, if they could,
court, which was not to be in session for full six months to come.
my trial. I had good counsel. There was not a particle of proof that
prosecution to produce my first wife, from whom I had separated, or,
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sentenced me to three years' imprisonment in the State Prison, at
confinement.
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