Re: [Embedded troll] Easy Questions

From: rickman (spamgoeshere4_at_yahoo.com)
Date: 05/06/04 

Date: Thu, 06 May 2004 12:01:44 -0400

buddy.spaminator.smith@ieee.org.invalid wrote:
>
> Guy Macon <http://www.guymacon.com> wrote:
>
> : [21] A man travels due south for one kilometer. He turns
> : left 90 degrees and travels due east for one kilometer, at
> : which point he shoots a bear. He then turns left 90 degrees
> : and travels due north for one kilometer, returning to the
> : exact spot he left from.
> :
>
> I've heard explanations of this, but i think the fact that you specified 90
> degrees for each turn makes it impossible anywhere...90+90+90 = 270
>
> For the north pole thing to work, it'd have to be 60 60 60 or some other
> combination that adds to 180.
>
> Am I wrong, or was the problem mistyped?

I am afraid that you have forgotten the basic assumptions of your high
school geometry and trig. They were both based on Euclidian geometry
which assumes you are working on a flat plane. On a sphere things work
a bit differently. For example, the surface of a sphere is a closed
geometry while a plane is an open one. You can go in any direction on a
plane and never return to your starting point. On a circle, if you keep
going in any one direction, you will return to your starting point.

The two turns are indeed 90 degrees each. But the angle at the pole can
actually be any angle between 0 and 360 depending on how far you walk
East. While walking East, you are not traveling in a straight line nor
are you on a great circle (closest thing to a straight line on a
sphere), you are walking the circumfrence of a circle defined by a
constant distance from the pole.

Like another poster said, think of this as a section of an orange or
look at a globe. Then assume that the 1 km takes you to the equator.
Clearly at the equator your 90 turn will truely take you east and a
second one will take you North again on a different longitude. 

-- 
Rick "rickman" Collins
rick.collins@XYarius.com
Ignore the reply address. To email me use the above address with the XY
removed.
Arius - A Signal Processing Solutions Company
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