Simple math question

  1. Leibniz says the following: "It is true, or rather it is necessary, that a circle is the most capacious of isoperimetric shapes, even if no circle really exists" in the opening line of a lengthy proof he gives for God's existence.

    I took calculus in college, but I don't recall what exactly these terms mean. By "most capacious" I assume he means having the most space in it, but what exactly are "isoperimetric shapes"? And why is a circle the most capacious of them? Google gives me nothing!
  2. jcsd
  3. micromass

    micromass 18,543
    Staff Emeritus
    Science Advisor

    I hope we're going to discuss math in this thread and not the existence of God.

    But anyway, I think you're looking for the isoperimetric inequality. Read this:

    It means that of all curves with a given perimeter, the circle has the greatest surface area.
  4. I'm still not sure I fully understand.

    Though any necessary geometrical truth will suffice for the proof of God in Leibniz. The full text is as follows:

    Still, I'd like to fully understand the example he gives.
  5. micromass

    micromass 18,543
    Staff Emeritus
    Science Advisor

    A lot of what you posted is philosophy, which cannot be discussed in a mathematics forum.

    Perhaps you can say specifically what you don't understand, because it's not very clear to me.
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