The mind of a mathmatician

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!"

Originally posted by chasparos
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!"

nothing incongruent in that!

Originally posted by chasparos
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!"

And we're proud of our captures!

Originally posted by TheMaster37
And we're proud of our captures!

And well we should be...
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)
:-)

Originally posted by TheMaster37
And we're proud of our captures!

As well we should be, since our mathematician hunter not only captured the lion he was seeking, but (hopefully for him) captured all of the lions currently in existence.

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.

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.

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?
Is i more in one than the other?

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?
Is i more in one than the other?

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 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.

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 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?

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?

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" you mean must be strictly separated by wolf of the other type. Build parallell fences in straight lines. Place wolves
CoD,SUC,CoD,SUC.

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.

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 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.

Yes I was being a bit simplistic.
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.

Well, remember how many sorts of wolf you have.

Originally posted by royalchicken
Well, remember how many sorts of wolf you have.

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.

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.

Oh, my bad. Under my rules, everything's pretty much equivalent to a chessboard, so you're right.

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.