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Arnold's Trivium
1991 Arnold's Trivium
70
Problem 70
Problem 70
Source:
July 1, 2010
geometry
3D geometry
sphere
Problem Statement
Calculate the mean value of the solid angle by which the disc
x
2
+
y
2
≤
1
x^2 + y^2 \le 1
x
2
+
y
2
≤
1
lying in the plane
z
=
0
z = 0
z
=
0
is seen from points of the sphere
x
2
+
y
2
+
(
z
−
2
)
2
=
1
x^2 + y^2 + (z-2)^2 = 1
x
2
+
y
2
+
(
z
−
2
)
2
=
1
.
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