Really this simple??

leitmotif · Jan 16, 2011

Got to calculating how much material I can put on a reel. Assume flat material whose width is same as reel ie not wire rope. Assume 1/2" thick such that one wrap is a change in diameter of one inch.

Here is what surprised me the change in circumferance per inch diameter change is 3.14 regardless of "starting diameter" ie circumferance change at 4 to 5 inch is same as that from 60 to 61.

Is it really this simple
circumberance change = Pi(D1 - D2)
or am I not thinking of something?

Dan Bentler

ndzied1 · Jan 17, 2011

There is an old riddle that goes something like this:

Imagine the earth is perfect sphere with a 25,000 mi circumference and someone has put a steel band tightly around the equator. I have cut the band and added 10 ft. of steel to the band creating a uniform space between the band and the surface of the earth. What is the largest animal likely to fit under the elongated band: an ant, a mouse, a cat, a man?

leitmotif · Jan 17, 2011

OK Norm with band and 10 extra feet concentric to earth there is a 1.59 foot gap so the asnwer could be either the cat or a man assuming the man belly crawls thru the gap.

Dan Bentler

Calistodwt · Jan 17, 2011

It's pretty obvious when you think about it?
Circumference = PI * D
So increasing D by 1 inch gives:
Circumference = PI* (D + 1) = PI*D + PI*1
Therefore increase in circumference = PI inches

MichaelG · Jan 17, 2011

Yep that simple

See http://mathforum.org/library/drmath/view/56481.html for Spiral calculations

leitmotif · Jan 17, 2011

The part that gets me is entuitively you would think there would be much greater difference in circumferance as you go out on wraps. But pi(D1- D2) holds true. Maybe the simpler things are harder to grasp or I just want to complicate it.

Thanks

Dan Bentler

RussB · Jan 17, 2011

ndzied1 said:
There is an old riddle that goes something like this:

Imagine the earth is perfect sphere with a 25,000 mi circumference and someone has put a steel band tightly around the equator. I have cut the band and added 10 ft. of steel to the band creating a uniform space between the band and the surface of the earth. What is the largest animal likely to fit under the elongated band: an ant, a mouse, a cat, a man?

Logic would say that if the cat would fit, so will the mouse and the ant.

ndzied1 · Jan 17, 2011

leitmotif said:
OK Norm with band and 10 extra feet concentric to earth there is a 1.59 foot gap so the asnwer could be either the cat or a man assuming the man belly crawls thru the gap.

Dan Bentler

Then do it again with the circumference of the moon..

RussB said:
Logic would say that if the cat would fit, so will the mouse and the ant.

That is why the problem said "largest..."

leitmotif · Jan 17, 2011

Russ B
Dominus Vobiscum eh?

How about
Oh fili mi beli bon(e?)

Dan Bentler

Really this simple??

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