Robert L. Read
It is a fact, perhaps surprising, that if you take any object and make an unbounded number of copies of it and always place a second copy in the same orientation to a first copy, the resulting collection of objects is essentially a helix.
This fact was “discoverd” during the Mathathon, and confirmed by a paper and private communication with Dr. Eric Lord. Since then, we have in fact worked out a Mathematica program that computes the radious and pitch of the helix based on only the intrinsic properties of the object joints.
Question at hand:
It would be nice if the function for the radius of this helix was given by a nice close-form expression of the length of the object and the angular relationship. In fact, there is such a formula, but it has about 50 terms. It is beyond human comprehension.
There are, however, ways we can still make use of this formula. For example, we graph special cases. Better yet, we can make software that allows you to enter the angular displacement and automatically computes (and renders in 3D) the object stacking the coincident helix induced by it.
This project spawned Project #45. This project is closed in favor of that project.