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Wednesday, 10 April 2013

Treasure Map

Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0 m, –20.0 m), B (60.0 m, 80.0 m), C (–10.0 m, –10.0 m), D (40.0 m, –30.0 m), and E (–70.0 m, 60.0 m). All of the points are measured relative to some origin, as in Figure. Long John’s map instructs you to start at A and move toward B, but cover only 1/2 the distance between A and B. Then move toward C, covering 1/3 the distance between your current location and C. Then move toward D, covering 1/4 the distance between where you are and D. Finally, move toward E, covering 1/5 the distance between you and E, stop, and dig.

A (30.0 m, –20.0 m), B (60.0 m, 80.0 m), C (–10.0 m, –10.0 m)
D (40.0 m, –30.0 m), and E (–70.0 m, 60.0 m).

The intermediate points are F,G,H and I. For each of coordinates x and y:
 F = A + 1/2 (B - A)
 G = F + 1/3 (C - F)
 H= G + 1/4 (D - G)
 I = H + 1/5 (E - H)

Vectors:
F = (30,-20) + 1/2 ((60,80) - (30,-20)) = (30,-20) + 1/2 (30,100) =  (45, 30)

 G = (45,30) + 1/3 ((-10,-10) - (45, 30)) = (45, 30) + 1/3 (-55, -40) =
= (45-55/3,30-40/3)
 
H= ... 

or you can use a program

XA=30.0
YA=-20.0
XB=60.0
YB=80.0
XC=-10.0
YC=-10.0
XD=40.0
YD=-30.0
XE=-70.0
YE=60.0
XF=XA+(XB-XA)/2.
YF=YA+(YB-YA)/2.
XG=XF+(XC-XF)/3.
YG=YF+(YC-YF)/3.
XH=XG+(XD-XG)/4.
YH=YG+(YD-YG)/4.
XI=XH+(XE-XH)/5.
YI=YH+(YE-YH)/5.
print *,XI,YI
output: 10. 16.



Treasure Island is an adventure novel by author Robert Louis Stevenson, narrating a tale of "buccaneers and buried gold". Traditionally considered a coming of age story, it is an adventure tale known for its superb atmosphere, character and action, and also a wry commentary on the ambiguity of morality—as seen in Long John Silver—unusual for children's literature then and now. The influence of Treasure Island on popular perception of pirates is vast, including treasure maps with an 'X', schooners, the Black Spot, tropical islands, and one-legged seamen with parrots on their shoulders.