Math/Geometry problem

[pokerfan]

This is kinda cool and an example of what I read in my spare time:

A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new direction which is not known to the fast boat. How should the pursuing vessel proceed in order to be sure of catching the other boat?

The amazing answer is that the pursuing boat should continue to the point where the slow boat would be if it had set its course directly for the pursuing boat when the fog set in. If the boat is not there, it should proceed in a spiral whose origin is the point where the slow boat was when the fog set in. The spiral must be constructed in such a way that, while circling the origin, the fast boat's distance from it increases at the same rate as the boat being pursued. The two courses must therefore intersect before the fast boat has completed one 360 degrees circuit. In order to make the problem reasonably practical, the fast boat should be capable of maintaining a speed four or five times as fast as the slow boat. Also, if the fast boat's speed remains constant, the spiral must be logarithmic.



http://mathworld.wolfram.com/TrawlerProblem.html

Of course, it only works if the target only changes direction once.

[jpgray]

1. Yeah, but what are the chances my jacks will hold up when an ace flops against two opponents?

:P

[pokerfan]

3. What's the probability an A, K, or a Q will flop when holding JJ?

In my experience, about 100%. :)

[DarkTirade]

4. Unless somebody bets big, I'd wait for the river.

[rug]

2. Are you in the Coast Guard?

[Ptah]

5. Beautiful

:thumbsup:

[UndertheOcean]

6. Gotta love math

[Tuesday Afternoon]

7. I guess you can't hear anything in the fog

and one should hope there is no flotsom and jetsom in the water and why is the boat after the other boat anyway? and Let us hope that they don't hit a shallow patch thereby inconviently grounding theirself...:yoiks:

[Dr. Strange]

8. Reminds me of the Bellman Forest Problem.

http://www.joma.org/images/upload_library/22/Ford/Finch645-654.pdf

Which reminds me of a Cure song.

http://www.youtube.com/watch?v=HY7wuV_C1oI

[pokerfan]

10. That is beautiful

Some additional references http://mathworld.wolfram.com/LostinaForestProblem.html">here.

The best problems are the ones most easily stated.

[Rabrrrrrr]

9. Now do the same problem with spaceships in 3-D space, traveling at relativistic speeds

Perhaps one might begin with airplanes just to get a start on the math.

[JVS]

11. The goal of piloting a ship is not to ensure collision.

[kick-ass-bob]

12. follow the engine sounds.

:D