B3D-Chapter 8

Irene Klein

It seems as though everything discussed in the previous seven chapters has come together in this one chapter with the introduction of Coordinate Geometry.

I thought that it was interesting that the sunflower head patterns exhibit the golden ratio. Is there a scientific reason for this?

Another topic in chapter 8 that I thought was interesting was the discussion of "quaternions." However, how exactly do they describe the motion of a pair of pendulums?

Finally, it was also very interesting that the discussion with complex numbers related back to Chapter 7. It states that there would be a two-dimensional surface in a four-dimensional space. Isn't this yet another example of a configuration space?

Prof. Banchoff's response.