Mathematical Paradoxes

• Gabriel’s Horn

  • A geometric figure that has finite volume but infinite surface area.

  • It is formed by revolving the curve around the x-axis.

    The function is:

    $$y=\frac{1}{x}$$

    And its domain is:

    $$x\ge 1$$

  • The volume of Gabriel’s Horn is finite, specifically (pi), but the surface area diverges to infinity.

  • Great video on Numberphile channel.