Thanks everyone, Tom, Warut, James. The significance of those integrals is that their summing to zero implies: [The geometric mean of the chord-lengths of all the chords containing some given point of the unit circle] = 1. Is there maybe a direct way to see that? —Dan

Dan Asimov writes:

...

Thanks! (That HAD to be true since no two real numbers can be as close as these were.)

—Dan

...

According to maple they are symbolically equal. I did not dig into it to try to see why.

On Mon, Aug 20, 2018 at 5:19 PM Dan Asimov <dasimov@earthlink.net> wrote:

...

Let f(x) = ln(2-2*cos(x))

Then are these two numbers equal?

A = -Integral from 0 to π/3 of f(t) dt

B = Integral from π/3 to π of f(t) dt

I can't tell. But they're extremely close.

—Dan

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun