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Putnam
1951 Putnam
B7
Putnam 1951 B7
Putnam 1951 B7
Source: Putnam 1951
July 6, 2022
Putnam
Volume
sphere
four dimensions
Problem Statement
Find the volume of the four-dimensional hypersphere
x
2
+
y
2
+
z
2
+
t
2
=
r
2
x^2 +y^2 +z^2 +t^2 =r^2
x
2
+
y
2
+
z
2
+
t
2
=
r
2
and the hypervolume of its interior
x
2
+
y
2
+
z
2
+
t
2
<
r
2
x^2 +y^2 +z^2 +t^2 <r^2
x
2
+
y
2
+
z
2
+
t
2
<
r
2
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