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Gabriel's Horn

​
revolution
360
maximum x
10
Gabriel's Horn is obtained by rotating the curve
y=
1
x
around the
x
axis for
1≤x≤∞
. Remarkably, the resulting surface of revolution has a finite volume and an infinite surface area. It is interesting to note that as the horn extends to
∞
, the volume of the horn approaches
π
.

Details

Snapshot 1: The equation
y=
1
x
for
1≤x≤∞
is used to generate the surface.
Snapshot 2: The surface is generated by rotation around the
x
axis.
Snapshot 3: Gabriel's Horn is formed by a complete rotation around the
x
axis.

External Links

Permanent Citation

John Snyder
​
​"Gabriel's Horn"​
​http://demonstrations.wolfram.com/GabrielsHorn/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007
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