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At 11:28 PM 6/13/2006,Herbert Prinz  wrote:
>George Huxtable wrote:
>
>>Replying to my posting stating-
>>|
>>| >The locus of an observer who was somewhere unknown on that circle becomes,
>>| >after that displacement, not a circle at all. It's distorted, and the
>>| >greatest distortion occurs in directions at 45 degrees (and 135, 225,
>>| >315 degrees) to the direction of travel.
>>
>>Herbert Prinz replied-
>>
>>| I don't understand this. Shifting the circles in an east-westerly
>>| direction does not distort them at all. Therefore shifting them
>>| north-south must distort them the most. No?
>>
>>Not so, Herbert. If you shift every point on a circle (or any other
>>geometrical figure) in an East-West direction by a certain number of
>>DEGREES, then its shape and size remain quite unaltered; that's true.
>>But it's not what we are doing here. We are shifting by a certain
>>number of MILES, East or West, ...
>George,
>
>Of course! I moved a penny across a celestial globe to visualize
>Zevering's procedure and forgot for a moment that this was exactly what
>I had argued against earlier!
>
>Where the use of Mercator is concerned, your proof of the deformation of
>the circle of equal altitude is correct. It is sufficient to refute
>Zevering's method by one counter example in a trivial case in which you
>don't need Mercator. But I wanted to go beyond this by outlining a
>constructive solution to Michael Dorl's problem for the general case. It
>was in this context that I brought up Mercator. This projection
>facilitates the advancement of a position along a loxodrome on a sphere.
>Therefore I think that it is intrinsically related to the nature of the
>deformation that any geometrical figure undergoes when shifted along a
>loxodrome. (It's this "scale ~ sec latitude" thing.) Or it could be that
>I am just hung up on this.

Don't know about that but there are many ways to skin a cat as the saying
goes.  I thought I did outline a method for advancing the equal altitude
circle.  Here's an interesting case.  Assume a equal altitude circle at a
few hundred miles in diameter that just falls short of the pole by say one
mile.  Now advance that circle by 6.28 miles west.  The circle grows a kind
of upside down J shaped figure with the hook of the J surrounding (but not
enclosing) the pole.  As you make the circle more closely approach the pole
and increase the advance distance, you can get a coil; kind of like
stirring paint.  (At first I though it might result in a figure eight but I
dissuaded myself from that view.)

Mike

>Herbert Prinz

   

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