Walking in a straight line
How to fold it inspired me to understand the Peaucellier’s linkage. Initially, I wrote a number of equations and rather foolishly (and lazily) asked Mathematica to solve them. This was not successful but taught me:
 about some of the algorithms used in solve
 a limitation of using Solve: this is more a failure to think about the problem deeply enough
I explored the Wolfram Demonstration Project and there was a project on the linkage. The source code was illuminating. I started thinking about how this solution was derived. Here is my approach. ( It never ceases to surprise me how often I took the wrong approach and how quickly a better approach is revealed. )
Consider the above diagram. Choosing suitable lengths for XA (=XB) and AC=BC=AD=BD one can solve for using
I will present this using a number of images (the WordPress is laborious):
I have also made an embedded CDF. The Wolfram Demonstration Project demonstration of Izidor Hafner referred to above is more instructive and shows another linkage that produces a straight line.

January 26, 2012 at 12:12 amStraight lines  Unkown Blogger Pursues a Deranged Quest for Normalcy

January 28, 2012 at 11:53 pmWalking in a straight line « Unknown Blogger Mathematica  Solve Math & Science Problems  Solveable.com