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The Grazing Goat: CR4 Challenge (09/15/08)

Posted September 14, 2008 5:01 PM

This week's CR4 Challenge Question:

A goat is placed in a fenced-in circular field with radius r. It is tethered to a point on the perimeter of the field by a rope which allows it to graze as far as the radius R. What is the value of R to the nearest cm, if the goat can graze exactly ½ the circular field area, and r = 10m

Thanks to SlideRuler for this question!

And the Answer Is....

The grazing area is segment ABC + segment ABD

Therefore ½*r²*(2θ-sin(2θ))+½*R²*(2Φ-sin(2Φ))=½*π*r². ... eq(1)

also we have θ+Φ+Φ = π (isosceles Δ origin,C,A) ... eq(2)

and r*sin(θ) = R*sin(Φ) (both equal to ½*AB) ... eq(3)

Replacing 2Φ with (θ-π); and replacing R with r*sin(Φ)/sin(θ); and using the relationship sin²(Φ) = ½*(1-cos(2Φ)) = ½*(1-cos(π-θ)) = ½*(1+cos(θ)) in equation (1) gives

(π-θ-sin(θ))+(2θ-sin(2θ)-π)*(1+cos(θ)/(2*sin²(θ))=0 ... eq(4)

This has only one variable θ, and the root can be found using Newton's approximation. x_n+1 = x_n - y_n/y'_n

Using a starting value of θ=1 gives successively

θ =1 --> 1.2143 --> 1.2327 --> 1.2354 --> 1.2358 --> 1.2359

and the corresponding values of R by using eq(2) to get Φ and eq(3) to get R; (remembering r=10m) are

R= 10m --> 11.41m -->11.56m --> 11.58m --> 11.59m --> 11.59m

The answer to the given problem is therefore 11.59m

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#8 "Re: The Grazing Goat: CR4 Challenge (09/15/08) " by CSM Engineer on 09/15/2008 12:45 PM (score 2)
#12 "Re: The Grazing Goat: CR4 Challenge (09/15/08) " by jim35848 on 09/15/2008 2:05 PM (score 5)
#23 "Re: The Grazing Goat: CR4 Challenge (09/15/08) " by carel on 09/16/2008 6:12 AM (score 2)

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#108 "Re: The Grazing Goat: CR4 Challenge (09/15/08) " by jdretired on 09/29/2008 3:41 AM (score 1)

Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#1 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 9:32 AM
	This page might help, but maybe there's a better way than grinding up equations. __________________ For sale - Signature space. Apply on self addressed postcard..
	Reply

ProcessEngr Active Contributor Join Date: Sep 2008 Location: Cambridge, MA Posts: 15	#2 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 9:50 AM
	R = 707 cm. Total area of the circle is 314.149 M2. 1/2 of that is 157.0796 M2. solve for R gives 7.07M = 707 cm. __________________ At the end of the day you have to live with the decisions you've made.
	Reply

Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#3 In reply to #2 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 10:08 AM
	If that's correct, then the goat can't even reach the centre of the field..... __________________ For sale - Signature space. Apply on self addressed postcard..
	Reply

Anonymous Poster	#4 In reply to #2 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 10:48 AM
	Kris is right. The area of the entire second circle would be half the area of the first. So the area that is inside both circles must be much smaller.
	Reply

ProcessEngr Active Contributor Join Date: Sep 2008 Location: Cambridge, MA Posts: 15	#5 In reply to #4 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 11:01 AM
	Right. If you check the area of the second circle is half of the first. Total area of a cicle is pi * radius **2. Calculate the area of the circle given the radius is 10 m. Then divide that by 2. That's half the total area. Take that area and back calculate the new radius. This gives the length of the tether. __________________ At the end of the day you have to live with the decisions you've made.
	Reply

Physicist? Guru Join Date: Apr 2007 Posts: 3531 Good Answers: 59	#6 In reply to #5 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 11:26 AM
	I think you are avoiding the intent of the question by assuming that the goat can jump over the fence and therefore graze the entire area of the circle defined by the tether. But the intent of the challenge is clear - that the goat can only graze inside the field, so only a part of the tethered circle is available for grazing. I don't believe that the challenge as intended can be answered without using some trigonometry - similar to the mathematica reference that Kris gave (can someone send me a smiley depicting a yawn?) It's quite straightforward to write the area in terms of the segments on either side of the line joining the points of intersection - and the angle subtended at the centre would be a suitable parameter. Nevertheless, I would be delighted if someone would prove me wrong about the practical need for trigonometry.
	Reply

ProcessEngr Active Contributor Join Date: Sep 2008 Location: Cambridge, MA Posts: 15	#7 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 12:23 PM
	You're right. I neglected to account for the fence. I have revised my answer: R= 1225 cm. You have one circle enclosing the other. Then A=pi(r1+r2)(r1-r2) where r1>r2. Area = 157.0794. r2 =10m. Back calculate r1. Sorry about not paying attention. Trying to do too many things at one time. __________________ At the end of the day you have to live with the decisions you've made.
	Reply

gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#16 In reply to #7 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 11:30 PM
	From your very few posts till now, it seems you tried to run fast, as if you wanted to win the race. CR4 is serious forum, always think more and more, and do not be hasty in reply. Your first answer was obviously wrong. I will try to reply other posts and agree / find accurate answer separately
	Reply

gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#17 In reply to #7 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 11:42 PM
	You new reply is also wrong. With R = 1225, the common area of two circles comes to 171.8044, which is not half the area of r= 10m.
	Reply

CSM Engineer Guru Join Date: Sep 2007 Location: Reno, NV (USA) Posts: 608 Good Answers: 66	#8 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 12:45 PM
	CAD says R=11.59m gives a crescent area equal to 1/2 the area of the fenced area. Don't care to prove it mathematically; I'm an engineer, not a math professor. __________________ Aequam memento rebus in arduis servare mentem.
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Anonymous Poster	#9 In reply to #8 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 12:58 PM
	That's a good guide, but not exactly satisfying (I know it makes no difference, but why state the half that the goat can't reach?)
	Reply

CSM Engineer Guru Join Date: Sep 2007 Location: Reno, NV (USA) Posts: 608 Good Answers: 66	#10 In reply to #9 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 1:06 PM
	Because "crescent" sounds better than anything I could come up with to describe the "funny squashed football-like" shape the goat can reach. __________________ Aequam memento rebus in arduis servare mentem.
	Reply Off Topic (Score 5)

Physicist? Guru Join Date: Apr 2007 Posts: 3531 Good Answers: 59	#11 In reply to #8 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 1:09 PM
	I must have made a silly mistake - my trigonometric answer came out at about 2-mm over 11.38-metres. (I wouldn't admit to this so quickly, except that I haven't time to work it more carefully at the moment)
	Reply

gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#18 In reply to #8 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:04 AM
	This answer is correct. Half the area of 10 m circle comes to 157.7965 and the area covered by goat with R=11.59m comes to 157.1391. Further refinement, though possible, not necessary
	Reply

jim35848 Power-User Join Date: Feb 2008 Location: Washington State Posts: 172 Good Answers: 31	#12 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 2:05 PM
	11.59 meters or 1159 cm. The area the goat can graze can be broken into two areas as shown below. Each of these areas can be found by subtracting a triangle from a pie shaped segment of a circle. If the half angle of the pie segment shown on the left is θ, the height of the common, vertical line segment is r sinθ. This gives an area of the segment bounded by the fence of r^2 (θ - sinθ cosθ). R is calculated as 2 r sin(θ/2) and the half angle of the other pie segment is β = (Π-θ)/2. The second part of the area is then β R^2 - r^2 (1 - cosθ)sinθ . Iterating to a solution, I get θ = 70.81 degrees (1.2359 radians) and R = 11.59 meters.
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CSM Engineer Guru Join Date: Sep 2007 Location: Reno, NV (USA) Posts: 608 Good Answers: 66	#13 In reply to #12 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 2:10 PM
	That's the approach I started with as well, but when I realized I would have to iterate the solution, I just went to CAD. I'll be interested to see if anyone comes up with a method to solve directly. __________________ Aequam memento rebus in arduis servare mentem.
	Reply

sahasushank Associate Join Date: Apr 2008 Posts: 50	#14 In reply to #13 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 3:26 PM
	Ive been trying half morning trying to calculate it using just math, without a calculator or excel for iterations or something else. Its driving me nuts. I dont think yu can do it, unless theres a property of kites that ive missed.
	Reply

GroovyCBR Power-User Join Date: Sep 2006 Location: Parry Sound, Ontario Canada Posts: 118 Good Answers: 1	#27 In reply to #12 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 9:33 AM
	This is what I came up with as well, but you put it into words better then I could. R=11.587 meters one thing no one has accounted for though is how stubborn and sneaky goats are. He is going to stretch out his neck to reach all the grass he can, and when he has gotten that he's gunna chew thru the rope and roam where he damn well pleases :D
	Reply

seulbog Associate Join Date: Sep 2008 Posts: 27	#33 In reply to #27 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 3:30 PM
	Darn sneaky goats!
	Reply

Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#34 In reply to #27 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 3:41 PM
	I'm not sure about all this..... Firstly, the conditions imply that the red area must be the same as the green area. (quadrant + green -red = quadrant -green + red) Second, Using your value Of R, I drew it on a cad program and calculated areas from output angles; My scale was 1/5, I'll go back to rectify the scale and check my calculations. The sections marked by the chord in the goats area came out as 3.3479 and 3.1298. Total is 6.4777, compared to field size of 12.56637. Maybe I made an error, but the 2nd diagram doesn't even look right if my statement about the coloured areas is correct. __________________ For sale - Signature space. Apply on self addressed postcard..
	Reply

EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#35 In reply to #34 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 4:08 PM
	Maybe it's because you were too careful coloring inside the lines? __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#38 In reply to #35 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 6:43 PM
	I get distracted so easily ! Anyways, I did it again and took the time to use a sensible scale. Checking R= 11.587 ; From this I get ; Area to right of common chord = 92.529 Area to left of common chord = 64.599 Grazed area = 157.128 Field area = 314.159 The program I used has some rounding up error, so I accept the answer given (even though the goat appears to be getting a bit extra). Now all I want is a better answer than messy iterations. Maybe I'll check Fyz's earlier quick calculation of R= 11.382 first (Fyz rarely errs, and a smaller R might work out better)...... __________________ For sale - Signature space. Apply on self addressed postcard..
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Physicist? Guru Join Date: Apr 2007 Posts: 3531 Good Answers: 59	#43 In reply to #38 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 5:56 AM
	I'm sure mine was an error entering numbers into the calculator (I think that makes me an errer). I used the same basic method as Jim. I'll come back to it when I have a sufficient run of free time (and use a spread sheet that leaves a clearer trail so I can check my numbers).
	Reply

EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#46 In reply to #38 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:16 AM
	"...Fyz rarely errs, and a smaller R..." I guess smaller errs are pretty much the same as rarer ones...it's mostly a matter of pronouncination now, anyway. __________________ Veni, vidi, video - I came, I saw, I got it on film.
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bob c Guru Join Date: Jul 2007 Location: Fort Lauderdale Florida Posts: 5708 Good Answers: 123	#49 In reply to #46 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:23 AM
	I prefer my errs medium rare. The smaller ones are easier to swallow. __________________ Bob
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Anonymous Poster	#50 In reply to #49 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:29 AM
	Errs are no that tough to chew. Perhaps try inserting your teeth before you eat?
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#51 In reply to #49 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:33 AM
	ROFLMSAO!!! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Anonymous Poster	#15 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/15/2008 11:00 PM
	R=7.07
	Reply

Anonymous Poster	#19 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:11 AM
	The radius of rope will be 10 cm.
	Reply

Anonymous Poster	#20 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:49 AM
	70.70 cm
	Reply

gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#21 In reply to #20 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:59 AM
	All guests here are not refering to answers earlier or playing dice
	Reply

Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#22 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 3:23 AM
	Here is a bit of a spoiler. Maybe someone can verify, draw, or explain it better. All these lunes are getting to me ! Hopefully anyone using the link to answer will confess. I would. __________________ For sale - Signature space. Apply on self addressed postcard..
	Reply

EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#24 In reply to #22 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 7:50 AM
	You would, but since I didn't see you answering, fortunately for you we don't need to hold you to your own standards. How's that for an ugly premise, eh? __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#28 In reply to #24 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:21 PM
	I'm still trying to understand jim35848's answer, and cope with the fact that I dislike iterative solutions. For now, I don't believe it's the only way so I shall continue to brood on it. Sadly my exploration of four squarable lunes has gone nowhere. Once I've arrived at a fantabulous big equation I shall post it without explaining the derivation, just to get your goat ! OK, make that 'if'. __________________ For sale - Signature space. Apply on self addressed postcard..
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sahasushank Associate Join Date: Apr 2008 Posts: 50	#29 In reply to #28 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:26 PM
	take R/r as Υ (gamma) and you should arrive at such a fantabulous big equation and then either use trial and error or iterate which is almost the same thing.... or just use MathCAD :P or Matlab
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#30 In reply to #29 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:39 PM
	Thanks sahasushank. The cogs in my head are turning..... __________________ For sale - Signature space. Apply on self addressed postcard..
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sahasushank Associate Join Date: Apr 2008 Posts: 50	#31 In reply to #30 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 12:45 PM
	you're welcome Another thing i can suggest is working in the coordinate system. what i mean is taking the center of the r=10 m circe as (x,y)= (0,0) and forming equations, ... x²+v²=r² & (x-10)²+y²=R² You'll need to use a bit of trigonometry as well. I had to. youll get a equation with cos^-1 and stuff. Dont put in any numerical values until you reahc the final equation. and solve for Υ
	Reply

EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#32 In reply to #28 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 1:39 PM
	Here y'go for a start... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#39 In reply to #32 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 10:02 PM
	Careful, now, or you might wind up with one of these: __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#45 In reply to #39 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:11 AM
	Actually, I kinda think I'd prefer that! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#54 In reply to #45 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 12:28 PM
	Are you sure? Those things are awful noisy! The mortar platoon of my National Guard unit had some. I remember they issued hearing protectors to the drivers because they would sit right next to the engine. __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#62 In reply to #54 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 5:09 PM
	Yeah, but I've seen 'em in action, and they go places even this guy would have trouble with! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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seulbog Associate Join Date: Sep 2008 Posts: 27	#55 In reply to #28 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 2:05 PM
	If it's an old goat, it just might be my mother-in-law. In that case please just open the gate and let her run. Thanx!
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carel Commentator Join Date: Apr 2007 Location: South Africa Pretoria Posts: 59 Good Answers: 4	#23 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 6:12 AM
	The area the goat grazes on can be divided into two areas. One governed by r=10 and the other by R. Summing the two areas by using integration I get R = 11.5872 See algorithm below procedure TForm1.Button1Click(Sender: TObject); var dx,x,r,a1,a2,at:real; waarde:real; begin waarde:=25pi; r:=strtofloat(edit1.text); x:=rr/20; dx:=1/1000000; a1:=0; repeat a1:=a1+dxsqrt(rr-xx); x:=x+dx; until x>r; a2:=0; x:=10-(rr/20); repeat a2:=a2+dxsqrt(100-xx); x:=x+dx; until x>10; at:=a1+a2; button1.caption:=floattostr(at); end;
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double_j_b Guru Join Date: Jan 2007 Location: Broken Arrow, OK, USA Posts: 838 Good Answers: 26	#25 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 7:59 AM
	I am just an old country boy but I can tell you one thing for sure. Goats is ornery critters and no matter whut you dew the darn thing always seem ta chew threw the darn tether and eat the whole ding dang field anyhow. So it jus don matter how long his tether is, cuz he gonna eat the whole dern thang. <toothless grin> __________________ If necessity is the mother of invention then is laziness the mother of necessity?
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llohf Participant Join Date: Sep 2008 Posts: 1	#26 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 9:32 AM
	Once I had a cow that I tied-up in this exact scenario. She was able to graze to a radius of almost 1159 cm. She was a good ol' cow.
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phoenix911 Guru Join Date: Aug 2007 Posts: 23359 Good Answers: 418	#36 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 5:16 PM
	Speaking of tethering goats. A friend of mine father had a authentic Swedish restaurant with grass for a roof. They would stake a goat on the roof and it would graze on it. When I was twelve I had a little league game and drove past the restaurant and saw Lars mowing his roof with a lawn mower. He missed the game the next time we played I asked what was he doing mowing the grass on his roof wheres the goat. He said that when he staked the goat on the roof he stake him too close to the edge and the goat jumped off. Unfortunately he also didn't stake the goat enough chain to touch the ground. (tonights special mutton) As a twelve year old and to this day, I still get that picture of the goat hanging there in my mind. At least now I don't bust out laughing. __________________ “ When people get what they want, they are often surprised when they get what they deserve " - James Wood
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gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#40 In reply to #36 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 10:51 PM
	If aim is to allow the goat to finish half the grass from 10m radius field, instead of roping him on a point on the fence, put the pole in the centre of the field and tie with rope of 7.07m long. You need not make so much of mathematical circus.
	Reply

EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#47 In reply to #36 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:18 AM
	Reminds me of a saying my Granddad used to use - "might as well be hanged for a sheep as a goat"! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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shooter Power-User Join Date: May 2005 Posts: 161 Good Answers: 2	#37 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 5:58 PM
	It appears that the question has been correctly answered, however, as a side bar, I agree with one of the other posts, the goat is going to graze the entire fenced in area. Why, you may ask? Because anyone who has ever staked out a goat in a field, or back yard, knows that you must use chain and not rope as stated in the challenge question. I had one staked on a chain and he grazed in a ever decreasing circular manner until all of the chain was wound around the stake. I ended up chaining him to a cement block that he could drag around and graze, but slowed him down enough that I could catch him.
	Reply

gsuhas Guru Join Date: Dec 2007 Location: 18 29 N 73 57E Posts: 1389 Good Answers: 31	#41 In reply to #37 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/16/2008 11:13 PM
	OH! I have same grass field of 10 m radius. By roping one goat to one point on fence, wit rope of 11.59m, I can finish grass of half the field. But I have two goats, and I want finish complete grass with 50:50 sharing. But by tieing other goat at dimetrically opposite point of the first goat, with rope of 11.59 m, I can not achieve the goal. There still remains some grass and some area in between is shared by both the goats simultaniously. My goats are in war here. Can anybody suggest the solution?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#42 In reply to #41 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 1:03 AM
	Keep the goat you had tethered in the centre at #40. Second goat has a shorter 2.93m leash, fixed to a free running ring on a perimeter rope. __________________ For sale - Signature space. Apply on self addressed postcard..
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Anonymous Poster	#44 In reply to #42 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 6:05 AM
	Might a straight fence down the middle be simpler? (and avoids the goats eating the ropes, or clunking chains in the middle of the night). (Personally, I'd either leave them both unchained in the field to get on with it, or remove them in turns. OK, they wouldn't each get precisely half the grass, but do we know that the different areas of the field are equally productive anyway?).
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#52 In reply to #44 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 10:09 AM
	It all depend on the unit cost of chain/fence. The committee also have to assess the maintenance requirements/life span of installation/H&S considerations blah blah blah.....I'd get rabbits anyway, they're less noisy and make good casserole/mittens. __________________ For sale - Signature space. Apply on self addressed postcard..
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Anonymous Poster	#53 In reply to #52 Goats versus Rabbits 09/17/2008 11:43 AM
	Please let us know when your first batch of rabbit's-milk cheese is ready for sale.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#63 In reply to #53 Re: Goats versus Rabbits 09/18/2008 3:32 AM
	The rabbit milk will be used in making Welsh Rarebit. Here's some bizarre stuff on rabbit milk ; http://news.bbc.co.uk/1/hi/health/852647.stm Transgenic bunny's can produce 10 litres of milk/year ; http://www.in-pharmatechnologist.com/Processing-QC/Milking-transgenic-rabbits-gets-approval __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#65 In reply to #63 Re: Goats versus Rabbits 09/18/2008 7:06 AM
	VERY interesting! Presumably the milkmaids have extremely small hands... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#66 In reply to #65 Re: Goats versus Rabbits 09/18/2008 12:20 PM
	10 litres/year is about 27 cc's/day. Aw.....it would fill just an egg-cup or two ! They must have Oompa loompa's for the milking. Check out the picture and info here - http://images.google.co.uk/imgres?imgurl=http://www.bioprotein.com/images/traite.jpg&imgrefurl=http://www.bioprotein.com/gb/faq.htm&h=120&w=120&sz=7&hl=en&start=13&usg=__84kG7Igc7g8Qmuo_VFk5-7tUpPM=&tbnid=faycF5S0c8kHxM:&tbnh=88&tbnw=88&prev=/images%3Fq%3Dmilking%2Brabbits%26gbv%3D2%26hl%3Den Scroll down here, they reckon it's more like 1/4 l/day for a good size doe. __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#67 In reply to #66 Re: Goats versus Rabbits 09/18/2008 12:46 PM
	And they use milking machines... Who knew? __________________ Veni, vidi, video - I came, I saw, I got it on film.
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bob c Guru Join Date: Jul 2007 Location: Fort Lauderdale Florida Posts: 5708 Good Answers: 123	#48 In reply to #41 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 9:21 AM
	Take the rope off the first goat. Convert the second goat into curried goat. __________________ Bob
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jt Guru Join Date: Jun 2007 Posts: 719 Good Answers: 25	#64 In reply to #41 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/18/2008 4:31 AM
	It's simple. Put them on shifts. Eating alternate days; or a day and night shift; Maybe they don't want to eat at night? (you'll need to speak to their union about this.) This will prevent them fighting, stop them getting fat and, give the grass time to recover. No problem. If they respond with bbaaa.. you'll know they are speaking a different language, are possibly immigrants, and can then refer them to another government department. jt.
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seulbog Associate Join Date: Sep 2008 Posts: 27	#56 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 2:26 PM
	I find myself with three basic thoughts after reading the responces to this challenge 1) As a tech type not an engineer type, I was very amazed with respoces to these challenges as to how quickly formulas were rememberd and used (as a tech type I haven't used many of the formulas since school some 20 years ago). I am not so amazed once I heard things like "I used the CAD" and suggestions to use computer math solvers (kinda like not cheat'n fair). 2) As a tech type I like to work smart not hard. So hats off to all you guys who work smart not hard. While I'm less amazed, I'm more impressed. 3) being a person who works smart not hard, why do we need to save half the grass. Let the goat eat all the grass so I don't have to mow the rest!
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phoenix911 Guru Join Date: Aug 2007 Posts: 23359 Good Answers: 418	#57 In reply to #56 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 3:26 PM
	As what was pointed out in an earlier post. dam Shepard used a rope, the goat ate through the rope. ate half the circle, then ate the other half. that ate the neighbors polygon that wasn't fenced in. then ate the little old lady's down the street and ate her quadratic Bush's. Then continued to the public park and ate the rose bushes planted in a triangle. after which the goat got bloated, foundered and died. __________________ “ When people get what they want, they are often surprised when they get what they deserve " - James Wood
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Anonymous Poster	#58 In reply to #57 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 3:37 PM
	Didn't the goat become irrational first?
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phoenix911 Guru Join Date: Aug 2007 Posts: 23359 Good Answers: 418	#59 In reply to #58 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 3:57 PM
	you calling me irrational __________________ “ When people get what they want, they are often surprised when they get what they deserve " - James Wood
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Anonymous Poster	#60 In reply to #59 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 4:16 PM
	Not unless your number's up - your avatar looks more pipe than goat, I think (unless it's a milk generator).
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#61 In reply to #58 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/17/2008 5:07 PM
	Pi's not irrational, that's cake you're thinking of... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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g srikanth Associate Join Date: Jul 2007 Location: Indore, India Posts: 53 Good Answers: 5	#68 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/20/2008 5:49 AM
	Mathematically the problem can be expressed as: ArcCos[R/(2r)]R^2+ArcCos[1-(R^2/(2r^2)]r^2-r(R^2-R^4/(4r^2))^0.5=(Pir^2)/2; which gives R~10.663 meters as a solution to the problem .
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#69 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/20/2008 5:54 AM
	Constucting around an equilateral triangle gives a fairly good approximate answer; That gives R=11.547, which ain't too far out. I'm at the end of my tether trying to find an 'easy' solution. __________________ For sale - Signature space. Apply on self addressed postcard..
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Anonymous Poster	#70 In reply to #69 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/20/2008 11:47 AM
	"end of my tether" Bite through it, just like Billy (or Jenny).
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#71 In reply to #70 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/20/2008 12:08 PM
	It's nice to have a bit of word-play appreciated ! Everyone can have a go-at it. __________________ For sale - Signature space. Apply on self addressed postcard..
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#72 In reply to #69 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/20/2008 1:51 PM
	I'm at the end of my tether trying to find an 'easy' solution. An easy solution doesn't exist. Anyone who says there is, is most likely yanking your chain. __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#73 In reply to #72 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/21/2008 2:59 AM
	I don't think anybody said there's an 'easy' solution, but why is it so ? I don't think there's an easy solution, but it's fun to think about it. Most of my time looking at this has been spent diverting to lunes and cycloids - the words seem so appropriate ! Going mad and running around in circles is great mental exercise. __________________ For sale - Signature space. Apply on self addressed postcard..
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#74 In reply to #73 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/21/2008 9:28 PM
	Going mad and running around in circles is great mental exercise. Now I know why you often use a squirrel as an avatar! BTW, what ever happened to the jumper? __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#75 In reply to #74 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 2:09 AM
	......Is that some kind of tangential thinking >>>goats>>>sheep>>>wooly jumpers ? There are two jumpers in my collection - the ghostly flying squirrel and Spring Heeled Jack of Olde Londone Towne. I feel a change coming on this morning.....decision in progress........ __________________ For sale - Signature space. Apply on self addressed postcard..
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Anonymous Poster	#76 In reply to #75 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 8:49 AM
	Dr. Squirrel and Mr Jack Hyde?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#77 In reply to #76 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 11:44 AM
	....some might say, "better the devil you know"....... __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#78 In reply to #77 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 12:00 PM
	While yet others might prefer "Dr. Jack and Mr. Squirrel Hide" - but we don't encourage their sort 'round these parts! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#79 In reply to #78 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 12:07 PM
	Squirrel Hide __________________ For sale - Signature space. Apply on self addressed postcard..
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#80 In reply to #79 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 3:38 PM
	Maybe this guy can help you get away: __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#82 In reply to #80 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/23/2008 1:36 AM
	Now you've got me worried about Rocky Road Ice Cream ! __________________ For sale - Signature space. Apply on self addressed postcard..
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#89 In reply to #82 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/24/2008 9:23 AM
	Now you've got me worried about Rocky Road Ice Cream ! Nothing to worry about, this guy has it covered! __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#91 In reply to #89 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 3:24 AM
	Hee hee....this one almost has it as well. __________________ For sale - Signature space. Apply on self addressed postcard..
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#97 In reply to #91 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 9:05 PM
	Ah, WB6ACU! I could listen to him all night long! __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#99 In reply to #97 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/26/2008 2:09 AM
	__________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#100 In reply to #97 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/26/2008 7:15 AM
	Yeah, not bad for a kid from Wichita, huh? __________________ Veni, vidi, video - I came, I saw, I got it on film.
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3Doug Guru Join Date: Jun 2007 Location: Kiefer OK Posts: 1325 Good Answers: 22	#102 In reply to #100 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/26/2008 3:16 PM
	Yeah, not bad for a kid from Wichita, huh? What do you mean by that? I'M from Wichita! Be keerful what you say about the town I wuz borned in! __________________ I wonder..... Would Schrödinger's cat play with a ball of string theory?
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#104 In reply to #102 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/26/2008 4:42 PM
	Hey, I LIKE Wichita - lived there from 1980-'85. Just Joe Walsh wuz also borned there... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#81 In reply to #79 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/22/2008 3:51 PM
	Here's the importance of punctuation at work. That should read: Squirrel, HIDE! __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#83 In reply to #81 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/23/2008 1:50 AM
	It's Del's battery making thread your current avatar needs to be wary of ! __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#84 In reply to #83 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/23/2008 7:06 AM
	I've a spare hat he may borrow... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#85 In reply to #84 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/24/2008 2:05 AM
	Dang - he's fled to Sicily ! The hat might also of been useful for Del's boiler problem. I'd hide if I were you, he might start dismantling you for all sorts of gadgets ! __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#86 In reply to #85 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/24/2008 7:00 AM
	I feel safe - I'm nowhere near Sicily. And if I need protecting from a cat, you know about Reginald...and his adoptive brother, Poti... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Anonymous Poster	#87 In reply to #86 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/24/2008 7:32 AM
	Really?
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#88 In reply to #87 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/24/2008 8:01 AM
	Niiice kitty, pretty kitty - here, play with this for a minute... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#90 In reply to #88 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 3:18 AM
	According to the TV, there are more Tigers in private hands than there are in the wild. The majority of privately 'owned' ones were said to be in Texas. It's only just around the corner from Florida.... __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#92 In reply to #90 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 7:59 AM
	There's a herd (flock?) of 'em in Las Vegas, NV, too. Interesting, lions come in "prides", but tigers are solitary - I don't know of a word for a group of 'em... __________________ Veni, vidi, video - I came, I saw, I got it on film.
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Anonymous Poster	#93 In reply to #92 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 10:18 AM
	The following terms are sometimes used: Streak, ambush, or hide. But I personally prefer the following unofficial collectives: a mating, a mother-and-cub, or (best of all, perhaps) a contradiction The picture (taken from Wikipedia) is of Indochinese Tigers
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Kris Guru Join Date: Mar 2007 Location: Etherville Posts: 12354 Good Answers: 115	#94 In reply to #93 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 11:51 AM
	I don't know where all these collective nouns originate. No Stenkin' Badgers ! __________________ For sale - Signature space. Apply on self addressed postcard..
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EnviroMan Guru Join Date: Nov 2007 Location: Gone to Alabama with my banjo on my knee... Posts: 5595 Good Answers: 20	#96 In reply to #94 Re: The Grazing Goat: CR4 Challenge (09/15/08) 09/25/2008 2:53 PM
	It lists a "cete of badgers". What is that? It is merely the nature of the beast. __________________ Veni, vidi, video - I came, I saw, I got it on film.
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#8 "Re: The Grazing Goat: CR4 Challenge (09/15/08) " by CSM Engineer on 09/15/2008 12:45 PM (score 2)
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The Grazing Goat: CR4 Challenge (09/15/08)

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