Re: [Embedded troll] Easy Questions

From: Guy Macon (http://www.guymacon.com)
Date: 05/06/04 

Date: Thu, 06 May 2004 11:10:27 -0700

Paul Burke <paul@scazon.com> says...
>
>buddy.spaminator.smith@ieee.org.invalid wrote:
>
>> I've heard explanations of this, but i think the fact that you
>> specified 90 degrees for each turn

...but I didn't specify straight lines for the sides. "Due East" is
not a straight line or even a great circle in most locations.

>> makes it impossible anywhere...90+90+90 = 270

...only for triangles. This isn't even close to being a triangle.

>> For the north pole thing to work, it'd have to be 60 60 60 or some other
>> combination that adds to 180.

...only for triangles. This isn't even close to being a triangle.

>> Am I wrong, or was the problem mistyped?
>
>The difference between plane and (approximately) spherical geometry- get
>a balloon and a marker pen and draw it out for yourself!

The difference between plane and spherical geometry does not bring
the hunter anywhere near to the same spot with one kilometer legs on
12,713.550 kilometer (pole to pole) geoid. It's the difference between
a great circle and a line of latitude that's important here. (lines of
longitude are all great circles, but only one line of latitude -
the equator - is a great circle).

>Actually, as the Earth is not perfectly spherical, he won't arrive
>exactly at the spot he started from,

I believe that you are incorrect, and that he will indeed arrive
exactly at the spot he started from (ignoring continental drift
and any quantum uncertainties...). I am unsure what term to use
to explain why. Perhaps the following will help:
(Plane --> Line / Sphere --> Great Circle / Geoid --> ?????? )

The key is that when he walks due east, he isn't walking in
a straight line or in a great circle or ?????? in plane, sphere,
or geoid geometry. To do that his first leg would have to reach
the equator instead of being one kilometer long. Once one
realizes that this "triangle" has a side that is curved rather
than straight, one sees that all triangle formulas (plane or
spherical or geoid) are useless.

(...and yes, I did have to get out my dictionary to get the right
spelling for "geoid"... <grin>) 

-- 
Guy Macon, Electronics Engineer & Project Manager for hire. 
Remember Doc Brown from the _Back to the Future_ movies? Do you 
have an "impossible" engineering project that only someone like 
Doc Brown can solve?  My resume is at http://www.guymacon.com/

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