#### Topic: Output path

Greetings to all! Once for a long time heard such task: someone appeared in wood without any navigation instruments and he needs to come out of the wood. On what path it needs to move, that is guaranteed to come out of the wood and also that it was an optimal path. Something such seems... Precisely I do not remember. Who knows this task prompt as it what its strict mathematical decision,  is precisely formulated also!

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: > Greetings to all! > Once for a long time heard such task: someone appeared in wood without any navigation instruments and he needs to come out of the wood. On what path it needs to move, that is guaranteed to come out of the wood and also that it was an optimal path. Something such seems... Precisely I do not remember. > Who knows this task prompt as it what its strict mathematical decision,  is precisely formulated also! Most likely it is the task "In dark wood" the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. The decision yet I do not result. Perhaps who that wants to think. As the task known the decision is possible and

#### Re: Output path

B> Most likely it is the task "In dark wood" B> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. No, it is other task. What distances it is not set. The wood form is not set.

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: B>> Most likely it is the task "In dark wood" B>> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. > is not present, it is other task. What distances it is not set. The wood form is not set. Upwards.

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: B>> Most likely it is the task "In dark wood" B>> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. > is not present, it is other task. What distances it is not set. The wood form is not set. The decision will not differ. The wood form "is not important" and in the task "In dark wood". And in what type distance it is necessary to set that, as a task statement in a type "it is necessary  to quit and on an optimal path" implies that the optimality of received decisions will be defined on distance which should be transited in the worst cases or as an average on all chances. If wood was authorized for inflating indefinitely it would be impossible to quit generally.

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: B>> Most likely it is the task "In dark wood" B>> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. > is not present, it is other task. What distances it is not set. The wood form is not set. We select any n (1). n steps strictly forward, then turn on the left on 90 (2). n steps strictly forward, then turn on the left on 90 (3). We increase n twice and goto (1)

#### Re: Output path

Hello, baily, you wrote: B> the Decision will not differ. The wood form "is not important" and in the task "In dark wood". Will be. B> and in what type distance it is necessary to set that as a task statement in a type "it is necessary  to quit and on an optimal path" implies, B> that the optimality of received decisions will be defined on distance Is not present, does not imply. I do not remember, what exactly meant under an optimality, can be that it is impossible to be returned in that point where we already were, something can still, but the distance is not mandatory.

#### Re: Output path

Hello, kov_serg, you wrote: _> It is sampled any n _> (1). n steps strictly forward, then turn on the left on 90 _> (2). n steps strictly forward, then turn on the left on 90 _> (3). We increase n twice and goto (1)) And it is the most optimal path? It is necessary to prove that the path is not present) is better

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: >) And it is the most optimal path? It is necessary to prove that the path is not present) Obviously that if we about "in dark wood", at first, it is necessary to depart on 1 km on a straight line is better.

#### Re: Output path

Hello, baily, you wrote: B> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. B> the Decision yet I do not result. Perhaps who that wants to think. As the task known the decision it is possible and  to Depart on kilometer on a straight line and to transit on a circle with center in a point of an initial finding?

#### Re: Output path

Hello, SomeOne_TT, you wrote: SO _> Hello, baily, you wrote: B>> the Boy lost the way in wood. Exactly in 1 km from it there transits road. The direction on it is not known only. Properly to go to the boy, to quit on road on the shortest path? Wood so dense that the boy sees road, only quitting on it. B>> the Decision yet I do not result. Perhaps who that wants to think. As the task known the decision is possible and  SO _> to Depart on kilometer on a straight line and to transit on a circle with center in a point of an initial finding? Where to take compasses, at night in dark wood, and than you are going to measure 1 km?

#### Re: Output path

E> it is obvious that if we about "in dark wood", at first, it is necessary to depart on 1 km on a straight line. And we not about "in dark wood", and about the initiating task) (Is formulated in the first message though and it is fuzzy) kov_serg wrote a path on which we is guaranteed come out of the wood. I simply wanted to find a source of this task both to look at the rigorous proof and to specify that meant under an optimality.

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: > And we not about "in dark wood", and about the initiating task) (Is formulated in the first message though and it is fuzzy) In the initial task not clearly that such is optimal", and that such to"come out of the wood", therefore in its frames that or it is impossible to prove... > kov_serg wrote a path on which we is guaranteed we come out of the wood. I simply wanted to find a source of this task both to look at the rigorous proof and to specify that meant under an optimality... It is actually clear that the good candidate for a path - a logarithmic spiral because it saves a corner to a direction start. So we google and on the first page we see... It?

#### Re: Output path

Hello, Erop, you wrote: E> In the initial task it is not clear that such is optimal", and that such to"come out of the wood", therefore in its frames that or it is impossible to prove... And I here also want to find accurate information and to look at the proof. In it and an essence of my first post. E> it is actually clear that the good candidate for a path - a logarithmic spiral because it saves a corner to a direction start. And what to us gives corner saving? Here corner saving, and extending circle bypass round center is basic not. It is possible to walk circles and a circle behind circle to increase circle radius. E> so we google and on the first page we see... E> It? That's just the point, what not it. Which I described the task in the first message it is possible . The primary source is interesting to me and whether there is for it a proved decision.

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: > And I here also want to find accurate information and to look at the proof. In it and an essence of my first post. I understand it, I do not understand your question about, whether precisely offered "the square-topped spiral" is optimal > And what gives us corner saving? Here corner saving, and extending circle bypass round center is basic not. It is possible to walk circles and a circle behind circle to increase circle radius. Well a broad gull. The spiral, does it somewhat optimally. E>> so we google and on the first page we see... E>> It? > That's just the point, what not it. Which I described the task in the first message it is possible . The primary source is interesting to me and whether there is for it a proved decision. And it not your task which you forgot/lost, unless?

#### Re: Output path

SO _>> to Depart on kilometer on a straight line and to transit on a circle with center in a point of an initial finding? _> where to take compasses, at night in dark wood, and than you are going to measure 1 km? Clearly that the boy has a smart phone with GPS

#### Re: Output path

Hello, Erop, you wrote: E> I understand It, I do not understand your question about, whether precisely offered "the square-topped spiral" is optimal Well I meant, what on such path we really quit, but me accurate information and the proof) E> And it not your task which you forgot/lost, unless interests? I fluently viewed that article which you sent - three cases there are considered: 1. A band of width l 2. A circle of diameter d 3. Half-plane the distance to edge and where here my task also is set?)

#### Re: Output path

Hello, Maxim Rogozhin, you wrote: E>> And it not your task which you forgot/lost, unless? > I fluently viewed that article which you sent - three cases there are considered: > 1. A band of width l > 2. A circle of diameter d > 3. Half-plane the distance to edge MR> and where here my task also is set?) well so to you is more visible that you read. IMHO, sensible enough analysis of variants. You another searched for something?