> The dimension of the configuration space of the juggling pin is six: the minimum number of parameters that specify the position in space is three, and the minimum number of parameters that specify an orientation is also three.<p>Can somebody explain this? Isn't the number of parameters that specify an orientation two, totaling five?<p>Pick two atoms in the pin and specify the location of one atom. Now the other atom can only be located on a sphere around the first atom. The sphere is a 2d surface for which you need two parameters.<p>Another problem is that you can encode two real numbers into one, for example by interleaving digits. So you could specify the entire pin with one real number. What exactly is the problem here and how can you eliminate it? You need to impose more conditions than simply continuity, because you can make a continuous bijection [0,1] <-> [0,1]^2?<p>I really like the approach of this book. I often don't feel like I understand (or even know what there is to understand) something until I code a program for it. For example you understand collisions if you can write a program that given an initial configuration of polygons at t=0, gives the configuration at later time. If you don't do this then you don't know exactly what you understand. Perhaps you understand collisions of point masses, but not general collisions.