Geometric puzzle - Pi mai pi mai tang tu...

hyree_hybrid

(Some may suggest this is in the wrong board but I insist to post it up here)

Say I have a bizarre travelling plan:

From where I start (point A), I wish to travel SOUTH 200km, then travel WEST 200km, then travel back NORTH 200km, and ultimately arrive at the departure point (point A)!

How can I do this? Where on earth can this happen? :re:

khairen

ntah...artic kot

cmf_aishiteru

north pole?

hyree_hybrid

Yep. North pole is one of them. Ada satu lagi.

sagiman91

(Some may suggest this is in the wrong board but I insist to post it up here)

Say I have a bizarre travelling plan:

From where I start (point A), I wish to travel SOUTH 200km, then travel WEST  ...
hyree_hybrid Post at 31-10-2009 11:49

u said u WISH to travel south...so...

u didnt said u go there...u just stayed at the point of the begining(point A)...

so 200 - 200 = 0km...

reez54

1# hyree_hybrid


hmm...looks like a triangular for me......

cmf_aishiteru

here's my take:

circumference of earth at equator, CE = 40,075.02 km
circumference at latitude L, CL = 200 km
latitude L: arccos(CL/CE) = 89.71 degree

now I want to find a point A (also in term of latitude), 200km above the latitude, L = 89.71 degree:

using the close form equation to find circumference, C = 2*pi*R
assume the radius of earth, RE = 6378 km to be uniform in all latitude
point A = 200km/RE = 0.03135 radian, or approximately 1.8 degree from L = 89.71 degree

Therefore, point A is 89.71 - 1.8 = 87.91 degree latitude

A is near South Pole!