A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion.
First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop.
Finally how far he is from his camp and in which direction?

• 9/64 + 9/16 =(9+36)/64 = 45/64
  sqroot(45/64)= 3root(5)/8= 0.839 miles from camp
• 14 years agoHelpfull: Yes(3) No(1)
• i+1/2j-1/4i-1/8j+1/16i....
  
  =4/5i+2/5j
  direction=tan(inverse)1/2
• 14 years agoHelpfull: Yes(3) No(2)
• He is in South Direction
  He is 1.125 miles from Camp
• 14 years agoHelpfull: Yes(0) No(1)
• 2 / root(5) miles in north east direction
• 14 years agoHelpfull: Yes(0) No(0)
• 4-20
• 14 years agoHelpfull: Yes(0) No(0)
• (0.5-0.125)= 0.375, (1.0-0.25)=0.75, sqrt(0.375^2 + 0.75^2)= 0.8385
• 14 years agoHelpfull: Yes(0) No(0)
• He is 3 root(5)/8 miles from his camp..
  i.e 0.84 miles from his camp
• 14 years agoHelpfull: Yes(0) No(0)
• The soldier is 0.8944 miles away from his camp towards East-
  North.
  
  It is obvious that he is in East-North direction.
  
  Distance travelled in North and South directions
  = 1/2 - 1/8 + 1/32 - 1/128 + 1/512 - 1/2048 + and so on...
  (a geometric series with r = (-1/4) )
  
  (1/2) * ( 1 - (-1/4)n )
  = ---------------------------
  ( 1 - (-1/4) )
  
  = 1 / ( 2 * ( 1 - (-1/4) ) )
  = 2/5
  
  Similarly in East and West directions
  = 1 - 1/4 + 1/16 - 1/64 + 1/256 - and so on... (a geometric
  series with r = (-1/4) )
  
  (1) * ( 1 - (-1/4)n )
  = ---------------------------
  ( 1 - (-1/4) )
  
  = 1 / ( ( 1- (-1/4) )
  = 4/5
  
  So the soldier is 4/5 miles away towards East and 2/5 miles
  away towards North. So using right angled triangle, soldier
  is 0.8944 miles away from his camp.
• 9 years agoHelpfull: Yes(0) No(0)