A pirate ship is persuing a merchant ship when a fog descends, obscuring the merchant ship in front. What path must the pirate ship take to guarantee intercepting the other ship? [the pirate ship can go 5x faster than the merchant, and the merchant can move in any direction as long as it's in a straight line].

ok, so the pirate needs to move in a straight line for a little bit, then move in an ever increasing spiral, a logarithmic spiral. r=a.e^(b.theta) and in parametric form x(t)=a.e^(b.t).cos(t), y(t)=a.e^(b.t).sin(t)

So im asking if there is an underlying ODE and if Maple can derive the above equations (and the numbers a and b).

the tv show i got this from displayed the following eq: t=d/(v1+v2).e^(theta/sqrt((v1/v2)^2-1))

BTW if you're an internet troll reading this, and don't believe this question belongs on this forum, other members might disagree.

hello

took this problem from a uk tv program.

4 dancers are initially at the 4 corners of a square, edge length 4 meters. every dancer moves towards the person on their left.

i want to know the equations of the spiral. the arc length of each path should be 4m.  also an animation of the 4 spirals would be great. 

dance.mw

under the heading "more spirals" the closest one is r(t)=1/t (decreasing modulus)

http://mathematische-basteleien.de/spiral.htm

A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is four times faster than the duck. Assuming the fox and duck pursue optimum strategies, is it possible for the duck to reach the edge of the pond and fly away without being eaten? If so, how?

http://www.crazyforcode.com/fox-duck-puzzle/

there is an animation here

https://www.youtube.com/watch?v=Zw9cHEnhzWo

wonder if the equations of motion can be derived usingg maple and an animaton...?

cheese_division.mw

3 different dia circular cheeses. same depth. minimize cuts such that its divided equaly among four people.

can be done in 3 cuts. can evem be done in 2

could some erudite richard provide maple solution to this Q. thx

reinstalled m18, i used to have an ini file, but it got deleted.

so i made a text file, called it maple.ini with the following text: 

interface(prompt=""):
e:=exp(1);
digits:=15;
HelpBGColor=255,255,224;
print("maple init loaded...");

I placed it

 C:\Program Files\Maple 18\bin.win

and

 C:\Program Files\Maple 18\lib

and

C:\Program Files\Maple 18\Users

it doesnt load when i load maple!