| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I spent the last 2 weeks reading this file from the beginning, and I have a puzzle problem for you all that I didn't see. While I was attending U. of Illinois, a friend of mine at MIT gave me this problem, and said it was on his homework for extra credit. I spent the next 2 years trying, occasionally, to solve it. I finally came up with a solution sometime later, but I don't have that available now. In case it is not readily apparent, I am no mathematician, though I can fool some people some of the time. A farmer has a round silo in the middle of a grassy area of radius R. He ties his cow to the door handle of the silo with a rope of length L. What is the area available for grazing? Please note that there are 2 cases, depending on whether L > pi * R or not. I am certain I could get a numerical solution via simulation, but when I actively worked this, I wanted an exact, symbolic solution. Enjoy. I'll try to find my notes on this and see if I was anywhere close...
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1582.1 | GAUSS::ROTH | Geometry is the real life! | Mon Mar 16 1992 21:34 | 6 | |
Interestingly, this problem has been mentioned recently in sci.math,
only it was a dog on a leash.
I haven't seen the solution or attempted to solve it though.
- Jim
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| 1582.2 | AUSSIE::GARSON | Tue Mar 17 1992 06:23 | 3 | ||
re .0
Does 907.* help? There it was a goat.
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| 1582.3 | re .2 - NOT! | GAUSS::ROTH | Geometry is the real life! | Tue Mar 17 1992 11:28 | 0 |
| 1582.4 | Partial solution. | CADSYS::COOPER | Topher Cooper | Tue Mar 17 1992 13:44 | 38 |
As it happens, this just came through the USENET.
Topher
------------------------------------------------------------------------------
From: daveb@hpgrla.gr.hp.com (Dave Boyd)
Newsgroups: sci.math
Subject: Re: Dog chained to a silo.
Message-ID: <2930012@hpgrla.gr.hp.com>
Date: 16 Mar 92 17:52:32 GMT
References: <6575@amsaa-cleo.brl.mil>
Organization: Hewlett-Packard, Greeley, CO
In sci.math, daveb@hpgrla.gr.hp.com (Dave Boyd) writes:
> L = length of the rope
> R = the _radius_ of the silo
> The area is then
> pi * L^2 L^3
> A = -------- + -----
> 2 3*R
> Dave Boyd
> Hewlett-Packard, Greeley, Colorado
> Standard Disclaimers Apply
Thanks to those who have pointed out that I solved the problem
only for the case that L <= pi*R. The original poster gave values
of L=10 and R=3.5, so I did solve his problem.
As L gets (very) large, A should approach pi * L^2. Maybe
someone would care to post a general solution?
Dave Boyd
Hewlett-Packard, Greeley, Colorado
Standard Disclaimers Apply
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| 1582.5 | Blush | AUSSIE::GARSON | Tue Mar 17 1992 20:51 | 7 | |
re .3
Silly me. I thought that the cow was inside the silo. After looking at
the solution I would guess that the cow is outside the silo. This
doesn't seem to be stated either way in .0 but on reflection I don't
suppose most farmers keep their cows in silos. As far as I knew a silo
is made from silicon. (-:
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| 1582.6 | TRACE::GILBERT | Ownership Obligates | Tue Mar 17 1992 21:14 | 62 | |
| 1582.7 | AUSSIE::GARSON | Mon Mar 23 1992 01:40 | 31 | ||
| 1582.8 | The Missing Triangle | VAXRT::BRIDGEWATER | Eclipsing the past | Tue Mar 24 1992 16:39 | 8 |
re: .7 .4 is correct for L <= pi*R. The mistake in .6 is that the area in the triangular area formed by the center of the silo and the two endpoints of the semicircle was never added in. This area is 0.5 * 2*L * R = L*R which cacels the -L*R term in .6. - Don | |||||
| 1582.9 | AUSSIE::GARSON | Wed Apr 01 1992 01:12 | 16 | ||