02 Sep '04 10:42

A mathematician is in Africa trying to capture a lion. When he spots one he proceeds to build a fence around himself and says, "I define this to be outside!"

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Out of my mind- Joined
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03 Sep '04 06:29

And well we should be...*Originally posted by TheMaster37***And we're proud of our captures!**

Consider all the hard work going in to spotting

the lion...

*There are many calculations required

to prove what were seeing**is]**infact a lion.

*Finding the optimal most cost effective path through

the terrain, maximizing probability of a lion coming in

range to be spotted.

*Chaos studies to determine probable paths of pray based on

statistical analasyis on probable weather conditions, to determine best grazing sites.

*Finding the right optical instruments to ensure fastest possible

survey of any area, minimized on the probability of missing a lion hiding in the grass..

a.s.o

(not to mention all calculations required on the fence itself)

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09 Sep '04 09:24

This might be a perfect way to study the essence of a lion.*Originally posted by Acolyte***There's a mathematical technique called 'lion-hunting' which goes like this: the hunter divides the world in two, and decides which side the lion is on. He then divides that half in two and continues for all eternity. As a result, the lion is contained in an arbitrarily small cage.**

Once the cage is smaller than the lion, You start running into

problems. in which part of this cage is the lion? Is it in both?

Is i more in one than the other?- Joined
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Your Kingside13 Sep '04 04:41

Isn't there a physics riddle dealing with Quantum Mechanics called "Schrodingers Cat" where using the probalistic nature of QM you don't know if the cat is dead or alive or both? Or something like that.....this is so off-topic, but I couldn't resist.*Originally posted by chasparos***This might be a perfect way to study the essence of a lion.**

Once the cage is smaller than the lion, You start running into

problems. in which part of this cage is the lion? Is it in both?

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Elsewhere13 Sep '04 05:11

Colin, can you solve the following related problem?*Originally posted by Acolyte***There's a mathematical technique called 'lion-hunting' which goes like this: the hunter divides the world in two, and decides which side the lion is on. He then divides that half in two and continues for all eternity. As a result, the lion is contained in an arbitrarily small cage.**

The Wolfpack are wandering around on some simply connected subset of the Earth's surface. Members of the Wolfpack can also be members of the Culture of Death and the Stand-Up Comedians, but don't need to be. Now, Ivanhoe is designing enclosures for the Wolves so that they don't start having fun at others' expense. He decides that the way to do this is to take a different subset of Earth's surface and make it into an internally subdivided enclosure by using continuous lengths of fence which initiate and terminate on the boundary of this area (they may self-intersect). Given that CoD wolves cannot be placed next to other CoD wolves because they howl in agreement and that SUCs cannot be placed next to SUCs for fear they may be confused with hyenas, which fence-configurations are possible? What if this takes place on a plane or some other surface? What if the surface is not orientable?- Joined
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13 Sep '04 08:11

If by "next to" you mean: Neighboring areas may not contain wolf of*Originally posted by royalchicken***Colin, can you solve the following related problem?**

The Wolfpack are wandering around on some simply connected subset of the Earth's surface. Members of the Wolfpack can also be members of the Culture of Death and the Stand-Up Comedians, but don't need to be. Now, Ivanhoe is designing enclosures for the Wolves so that they don't start having fun ...[text shortened]... s takes place on a plane or some other surface? What if the surface is not orientable?

same type.

Then start building a fence on the edge.. Build it in a loop. Place any wolf in the containment created. go straight. build another loop not intersecting or tangenting any other previously constructed loop(Insufficient english vocabulary) aso.

However if by "next to" you mean must be strictly separated by wolf of the other type. Build parallell fences in straight lines. Place wolves

CoD,SUC,CoD,SUC.- Joined
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Elsewhere13 Sep '04 08:14

I was unclear. I do mean that neighboring areas may not contain wolves of the same type. I am asking for a general classification of which fence-configurations can accomplish this and which can't, rather than a particular method, althoug yours is valid.*Originally posted by chasparos***If by "next to" you mean: Neighboring areas may not contain wolf of**

same type.

Then start building a fence on the edge.. Build it in a loop. Place any wolf in the containment created. go straight. build another loop not intersecting or tangenting any other previously constructed loop(Insufficient english vocabulary) aso.

However if by "next to" yo ...[text shortened]... olf of the other type. Build parallell fences in straight lines. Place wolves

CoD,SUC,CoD,SUC.- Joined
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13 Sep '04 08:39

Yes I was being a bit simplistic.*Originally posted by royalchicken***I was unclear. I do mean that neighboring areas may not contain wolves of the same type. I am asking for a general classification of which fence-configurations can accomplish this and which can't, rather than a particular method, althoug yours is valid.**

I don't know any names of patterns but:

If no empty enclusures are allowed no

three arbitrarily chosen areas can be each others

neighbors.

I also assume areas are considered neighbors

if they have any point on their boundary in common.

That is, even a corner.

If both above are true, I can see no other

solutions than having no intersections at all except

those on the edge of the containment area.

since you can't have a corner (intersection) with less than

three areas.

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13 Sep '04 18:16

2 sorts of wolf => Any fence pattern which divides the area into regions which can be coloured with two colours such that no two regions of the same colour are adjacent.*Originally posted by royalchicken***Well, remember how many sorts of wolf you have.**

Given your fence laying rules, I'm not sure that it is possible to construct a division which can't be coloured like that.- Joined
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Elsewhere13 Sep '04 19:10

Oh, my bad. Under my rules, everything's pretty much equivalent to a chessboard, so you're right.*Originally posted by iamatiger***2 sorts of wolf => Any fence pattern which divides the area into regions which can be coloured with two colours such that no two regions of the same colour are adjacent.**

Given your fence laying rules, I'm not sure that it is possible to construct a division which can't be coloured like that.

Suppose the fences can be placed however Ivanhoe wants provided he divides the enclosure into unambiguous regions. Also, wolves can be CoD, SUC, neither or both.