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Simple math question 
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#1
Apr214, 12:17 AM

P: 2

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
Apr214, 12:20 AM

Mentor
P: 18,345

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: http://en.wikipedia.org/wiki/Isoperimetric_inequality It means that of all curves with a given perimeter, the circle has the greatest surface area. 


#3
Apr214, 12:34 AM

P: 2

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


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