Chief Delphi - numerical computation contest

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- - numerical computation contest (http://www.chiefdelphi.com/forums/showthread.php?t=110034)

Ether

16-12-2012 21:19

Re: numerical computation contest

Quote:

Originally Posted by Bill_B (Post 1202425)

This whole thread reminds me of an easy (for you all) geometry question. Imagine a sphere the diameter of the Earth. Add to that a belt around the equator that has no space between it and the surface of the sphere. By how much must the length of that belt be increased to allow a playing card to be slipped underneath the belt at all points along it?

That problem has a simple explicit closed-form solution.

C = pi*d

C' = pi*d' = pi*(d+2t)

C'-C = pi*(d+2t) - pi*d = pi*2t

... where "t" is the thickness of the card.

Richard Wallace

16-12-2012 21:23

Re: numerical computation contest

Actually this problem is considerably more practical:

Imagine a steel rail one mile long, pinned to earth at points A and B one mile apart. The rail is warmed by about thirty Fahrenheit degrees, so that it elongates by one foot, causing it to deform from its original straightness into a circular arc. How far does the arc deviate from the original line, at a point halfway between A and B?

Bill_B

16-12-2012 22:19

Re: numerical computation contest

Quote:

Originally Posted by Ether (Post 1202427)

That problem has a simple explicit closed-form solution.

C = pi*d

C' = pi*d' = pi*(d+2t)

C'-C = pi*(d+2t) - pi*d = pi*2t

... where "t" is the thickness of the card.

I told you it was easy! What usually hangs fledgling geometers is the "2t" to allow the card under on both sides of the sphere. Everyone else just guesses "big" numbers because the sphere is so big.

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