THE SHAPE OF DIRICHLET REGIONS IN A COXETER LATTICE AS A FUNCTION OF DIVERGENCE AND RISE

The following sections are included:

• Introduction

• Simple Continued Fractions: Definition and Notation

• The Principal Convergents

• The Klein Lattice

• Intermediate Convergents

• The Coxeter Lattice

• ‘Heads’ and ‘Tails‘ of a Continued Fraction

• Shape and Squashing

• Optimal Squashing

• Intermediate Convergents and Near Maximum Elongation

• Disc Phyllotaxis

• Conclusion

• Acknowledgement

• Appendix A: Zero Squash and Varied α

• Appendix B: Some Textbook Formulae

• Appendix C: Full Squash and Maximum Elongation

• References