Riddles

JoeB-

I agree that my original point is wrong.


Some observations.
The 'center' isn't referred to in the original description.
Instead, distances from the edge are mentioned. So the center is the furthest point from the edge. There can be several centers,.. each then being a local center if you like.

Moving from one local center to another does always require 'going out' of the wood... by definition.
(in other words, if it was possible to move from a local center further into the wood then the center would not have been the center at all !!!)



The center doesn't need to be a single point. It could be a line. In which case, it'd be possible for a walker to be entirely within the wood, and to walk continuously but yet never go further into the wood, or out of the wood.



edited to add:
Original description
3. Just to be clear, let's make the reasonable definition that "going into the wood" means moving farther from the edge and "going out of the wood" means going closer to the edge. Now, can you think of how you might start walking into the wood, reach a point where you can't go any further in any direction without coming out of the wood and still not be as far into the wood as someone else is?

Mellor

JoeBallantine wrote: »

Some observations.
The 'center' isn't referred to in the original description.
Instead, distances from the edge are mentioned. So the center is the furthest point from the edge. There can be several centers,.. each then being a local center if you like.

I was understand that the centre was the answer, not the question.

Are we talking about different questions?


Moving from one local center to another does always require 'going out' of the wood... by definition.
(in other words, if it was possible to move from a local center further into the wood then the center would not have been the center at all !!!)

The center doesn't need to be a single point. It could be a line. In which case, it'd be possible for a walker to be entirely within the wood, and to walk continuously but yet never go further into the wood, or out of the wood.

As in a rectangular wood.

jack747

I've got one if a tree fell in a forest did anyone hear it. lol..rofl

JoeB-

Mellor wrote: »

....
As in a rectangular wood.

Does a rectangular wood have a center that's a single point?, or a line?

I'd have thought that the rectangle center is a single point.

I'm still not convinced that the whole wood thing works,.. and it might well revolve around whether or not the center of a rectangle is a line or a point.


The reason I think that the center of a rectangular wood is a point is that if we allow it to be a line, .. then when one stands on the endpoint of the line they could move towards the midpoint of the line,.. and by so doing they are moving further away from the (short) edge of the rectangle while remaining at a constant distance from the long side. Hence they would appear to be 'going into' the wood.

So a rectangular wood only has a point as the center, similar to a circular wood, or a square wood.



It's possible to have a center represented by a line, and the line need not have an end either.

Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.

1100010110

Would a spiral path approaching the centre of a circular wood not work? And to the mathematicks out there, is that an infinite distance?

Mellor

JoeBallantine wrote: »

Does a rectangular wood have a center that's a single point?, or a line?

Depend on how you (or the question) define centre.
Centre of area. It's a point.
Distance from the edge. It's a line.
Distance from all edges is prob a point.

I'd have thought that the rectangle center is a single point.

I would too. In normal circumstances.
I'm still not convinced that the whole wood thing works,.. and it might well revolve around whether or not the center of a rectangle is a line or a point.

The reason I think that the center of a rectangular wood is a point is that if we allow it to be a line, .. then when one stands on the endpoint of the line they could move towards the midpoint of the line,.. and by so doing they are moving further away from the (short) edge of the rectangle while remaining at a constant distance from the long side. Hence they would appear to be 'going into' the wood.

But they aren't going any further into the wood, the distance to get out is not increasing.

Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.

Distance from edge is a circle
Centre of area is a point in the centre of the ring.

1100010110 wrote: »

Would a spiral path approaching the centre of a circular wood not work?

I what what would that work?
I think people are talking about different questions.

And to the mathematicks out there, is that an infinite distance?

No. Why would it be.

1100010110

Mellor wrote: »

I what what would that work?
I think people are talking about different questions.

How far into the woods can you walk? Was that not the question?

Mellor wrote: »

No. Why would it be.

f(x) y=square root x?

1100010110

Mellor wrote: »

I what what would that work?

What? Wot wot? 5.01am you say?

Mellor

1100010110 wrote: »

How far into the woods can you walk? Was that not the question?

Yes
Your suggestion is a long route to the centre. But it gets no further in. Walking around in circles also a long route, but doesn't get far in.

f(x) y=square root x?

Each revolution of the spiral gets shorter so the function needs to approach zero.

Eg
1 +1/2+1/2...to infinite = 2

1100010110 wrote: »

What? Wot wot? 5.01am you say?

2pm actually, so can't even use the time as an excuse

1100010110

Surely a spiral path from any point on the edge of a circular woods approaching the centre is constantly getting further from the edge?
And so the distance travelled into the woods is constantly increasing, and if it approaches but never reaches the centre then it is an infinite distance?

I think I'm just taking the "how far can you travel into" part of the puzzle and trying to find that,
which would be an infinite distance on a spiral path into a circular wood which approaches but never reaches the centre.

My bad on the time, was just a bit confussed and presumed without checking the available facts.

JoeB-

Mellor wrote: »

Joe Ballantine said 'Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.'

Distance from edge is a circle
Centre of area is a point in the centre of the ring.

This is the reason I brought this up. The center of the wood can hardly be outside the wood, as it would be if it was in the exact center of a doughnut shaped wood. So the 'center' that fits the description given must be the circle. (i.e equal distance from edges)

The original statement mentioned going into and going out of the wood, but it didn't define the center itself.
We have since half defined the center to be a point where you cannot go further into the wood, without first going out of the wood. (There can be several centers)





The spiral path is new to me.

Can a path of infinite length be drawn in a finite circle? Is this a non-overlapping path?

A toilet roll cannot be infinite in length. (for a given thickness of roll and paper) as the paper itself has thickness. A thinner paper would take up less room.

So the length of a spiral path into the wood would depend on the thickness of the path, and whether it can be overlapping or not. Overlapping is likely not allowed. A path of zero width is not possible. So an infinite path is not possible.






Incidentally, can anyone give a formula for the thickness (diameter) of a toilet roll, given the length of the paper R say, and the thickness of the paper, T say, and the diameter of the paper core, say D. Can the diameter of the resulting roll be given in terms of R,T and C?


Say R = 50 meters = 50,000 mm
T = 1mm
C = 40mm

Final thickness of roll = ???

I think this is hard enough. I can approximate an answer handily enough, with one assumption made. I may need to use a spreadsheet to help.

To get an exact answer is tougher,
(no answer given here, but some observations)

especially if it's considered that the diameter of the roll is constantly increasing, requiring calculus to be used I'd imagine.

Constantly increasing in diameter as opposed to only increasing in a single step once per revolution, in which case an arithmetic progression rather than calculus might be useful.