Chapter 19 Geometry of the Perrin Sequence

The plastic number is a mathematical constant which is the real irrational solution of a monic cubic equation.  It is also the limiting ratio  Pn/Pn-1 of the Perrin and Padovan sequence of numbers.  Equations of degree 3 are not solvable by plane geometric projections using a compass and ruler.  A 3D solution to the problem is possible using paper folding or Origami techniques.  This Chalkboard demonstrates a construction of the plastic number and also its positive and negative powers.  The angle of trisection also contains information on powers of this irrational number.  It is also shown that the Perrin sequence and Padovan sequence are generated from the unit measure and powers of the plastic number.

Geometry of the Perrin_ and Padovan_ Sequences___






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