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Guest Message by DevFuse
 

bonanova

Member Since --
Offline Last Active Today, 04:26 PM
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Posts I've Made

In Topic: Upside Down Cake

28 October 2014 - 08:18 PM

 

 

Finite.

 

 

:unsure: Ok, I give up

 

 

Spoiler for


In Topic: more simple circles

27 October 2014 - 11:58 PM

You are correct, gavinksong. I did make an error.  I suppose it is possible to find a function by mapping the the values and using extrapolation to find the polynomial, but I do not know if this has yet been done.

 

For small numbers of circles the cluster is lumpy and erratic. One would expect an answer that is pretty much ad hoc. Which is to say that for the first n circles, it would take close to an nth degree polynomial to give a good approximation to the smallest bounding radius. A table would be just as good.

 

By the same token, I'd bet there's a fairly simple asymptotic solution for large values of n.


In Topic: Six sixes to make 1,000 (modified version)

27 October 2014 - 11:48 PM

@DejMar (and everyone.)

Thanks for your contributions.

They are the life blood of the site.


In Topic: Inner area

27 October 2014 - 11:43 PM

If we use non-integer radii does the inner area approach an irrational number?

 

With probability 1 it is irrational for circles of any radii -- integer or otherwise.

 

The area of a unit circle is pi.

The included area of three unit circles involves sin(60o).


In Topic: Inner area

27 October 2014 - 10:35 PM

FWIW:

 

The median area of 0.95248  was obtained for radii of (2 2 4) inches.

The next larger area 0.955875 was obtained for radii of (1 1 5) inches.

The next smaller area 0.858358 was obtained for radii of (1 4 5) inches.