The Infinity Paradox Of Gabriel's Horn

Gabriel's horn is made by rotating a graph of the function y = 1/x (when x is greater than or equal to 1) about the x-axis. Its surface area is infinite, but its volume is not-theoretically, the horn could be filled with pi cubic units of paint, whereas you'd need infinite paint to coat its surface.

Key Facts In This Video

  1. The Hilbert Hotel is a hotel with infinite rooms and infinite guests. The paradox asks the question, what happens if more guests arrive? 00:07

  2. The Painter's Paradox asks if one could theoretically paint the inside of Gabriel's horn, which has an infinite surface area but a finite volume. 02:10

  3. The "double your money" paradox asks how much money you should pay to enter a casino game in which a coin flip either doubles the pot or gives you the pot. 06:12

Written by Curiosity Staff November 24, 2015

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