Reciprocity ("Symmetry") Approach to Coin Dragon

 The heuristic Repricocity involves the idea that if a situation involves two components, A and B say, try looking at it both from the perspective of the relationship of A to B and from the perspective of the relationship of B to A.

Sir Isaac Newton really loved Reciprocity -- he kept applying it whenever he could. Thus Newton propounded: So here is a Reciprocity attack on the Coin Problem:

From the point of view of the red coin, the blue coin rolls about it until the point of contact has moved through 180 degrees.
But by symmetry
From the point of view of the blue coin, the red coin rolls about it until the point of contact has moved through 180 degrees.
That is, on both coins the point of contact has moved through 180 degrees, so that one coin is sitting on top of the other, both with the same heading as before.

A different turn of phrase is:
that just as the blue coin rolls around through half its circumference to reach the bottom of the red coin, then from the perspective of the blue coin, the red coin is rolling about it through half its circumference, so is now on the opposite of the blue coin to the initial state.

The powerful Reciprocity attack in terms of "point of contact" was supplied to me by the same (former) MIT professor who in interview in 1974 gave that very compelling Process attack on the Milk Bottle Problem, ("Milko"), as reported in Harvey A. Cohen, The Art of Snaring Dragons , MIT Artificial Intelligence Laboratory Memo 338, May 1975.

For comparison see::

Heuristic Process motivated attack on the Coin Problem
Einstein's solution to the Coin Problem
Homepage for the Coin Problem
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