Difference between revisions of "Gabriel's Horn"
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(ElWisty's writings were never really cleaned up.) |
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| − | '''Gabriel's horn''' is the [[surface]] obtained by revolving the [[graph]] of <math>y = 1/x</math> for <math>x \geq 1</math> about the <math>x</math>-axis. It | + | '''Gabriel's horn''' is the [[surface]] obtained by revolving the [[graph]] of <math>y = 1/x\,</math> for <math>x \geq 1</math> about the <math>x</math>-axis. It is noteworthy for having [[infinity|infinite]] [[area]], but enclosing a [[finite]] [[volume]] (in the region with <math>x \geq 1</math>) of <math>\pi\,</math> cubic <math>\mathrm{units}</math>. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 19:51, August 24, 2013
Gabriel's horn is the surface obtained by revolving the graph of <math>y = 1/x\,</math> for <math>x \geq 1</math> about the <math>x</math>-axis. It is noteworthy for having infinite area, but enclosing a finite volume (in the region with <math>x \geq 1</math>) of <math>\pi\,</math> cubic <math>\mathrm{units}</math>.