Gabriel's Horn or Torricelli's Trumpet

Gabriel's Horn or Torricelli's Trumpet

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Medium:  Paradox
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Release Message:  A geometric figure, which has infinite surface area but finite volume. Authored by Evangelista Torricelli.
Description:  A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals are covered by a finite area, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk "the wrong way" around the set to reach a nearby point). This can be represented by a Klein bottle.