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Miklós Schweitzer
1955 Miklós Schweitzer
9
9
Part of
1955 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1955- Problem 9
Source:
10/8/2015
9. Show that to any elliptic paraboloid
φ
1
\varphi_1
φ
1
there may be found an elliptic paraboloid
φ
2
\varphi_2
φ
2
(other than
φ
1
\varphi_1
φ
1
) and an affinity
ϕ
\phi
ϕ
which maps
φ
1
\varphi_1
φ
1
onto
φ
2
\varphi_2
φ
2
and has the following property: If
P
P
P
is any point of
φ
1
\varphi_1
φ
1
such that
ϕ
(
P
)
≠
P
\phi(P) \neq P
ϕ
(
P
)
=
P
, then the straight line connecting
P
P
P
and
ϕ
(
P
)
\phi(P)
ϕ
(
P
)
is a common tangent of the two paraboloids. (G. 18)
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