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Topic: I was the first to define a general formula for all area, volume
and hypervolume.

Replies: 4   Last Post: Nov 12, 2017 8:19 AM

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Posts: 5,511
Registered: 9/25/16
Re: I was the first to define a general formula for all area, volume
and hypervolume.

Posted: Nov 8, 2017 12:00 PM
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The arithemtic mean, in the infinite case, is
also an integral. Namely you have:

F(b) - F(a)
AM = -----------, where F(x) = integ f(x) dx
b - a

AM was used by Newton to derive the e^x formula.
AM has a nice property, you can estimate:

AM = f(c) for some c in (b,a)

Which gives further bounds, for example for a montonic
funtion that we have:

f(a) =< AM =< f(b)

But this still no way to get rid of limit or
infinite series.

Am Mittwoch, 8. November 2017 13:59:18 UTC+1 schrieb John Gabriel:
> Read the second New Calculus abstract and take the quiz:
> Quiz:
> Which of the following statements are TRUE?
> [A] The Ancient Greeks foresaw John Gabriel's genius but only got as far as defining plane number and solid number.
> [B] Area is properly defined as square units.
> [C] Area is properly defined as the product of arithmetic means.
> [D] Area is properly defined as triangular units.
> [E] Area can't be properly defined without the arithmetic mean.

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