Hello, John!
Some people found a treasure map, authenticated it and now looking for it.
Here's what it says:
"Start from the tree, walk directly to the falcon-shaped rock.
Count your paces as you walk.
Turn a quarter-circle to the right and walk the same number of paces.
When you reach the end put a stick in the ground.
Return to the tree and likewise walk to the owl-shaped rock, again counting your paces.
Turn a quarter-circle to the left, walk the same number of paces,
and put another stick in the ground. Connect the two sticks with a rope.
The treasure is beneath the midpoint of the rope."
HOWEVER, the tree was no longer on the island.
All that was left was the two weird-shaped rocks.
The people gave up looking for the treasure.
Did the people give up too soon?
Is it possible to find the treasure without the tree? . . . . Yes!
This is a classic problem. Code:
Q
X o
P o |*
o | | *
*| | | *
* | | | *
* | | | *
* | | | *
* | | | *
* | B | | *
F o------*----*-*----*--------o O
* A | C D *
* | *
* | *
o
T
We start at 
, walk to 
, turn 90° to the right,
. . and walk to point 
, where 
.
We start at , walk to 
, turn 90° to the left,
. . and walk to point 
, where 
.
The treasure is buried at 
, the midpoint of 
.
Draw perpendiculars 
to 
.
Since is the midpoint of , 
is the average of 
and 
.
. . That is: . 
.[1]
We find that: . 
.[2]
We find that: . 
.[3]
Substitute [2] and [3] into [1]: . 
Hence, the "height" of is half of the distance between the two rocks.
Since is the midpoint of , it follows that: 
is the midpoint of 
.
From the congruent right triangles: . 
and 
. . That is, the two end segments of are equal.
Hence, is the midpoint of .
To locate the treasure , we don't need the tree.
Locate , the midpoint of .
From , walk perpendicular to a distance of 
. . and there is the treasure!
LinkBack URL
About LinkBacks
