Harmonic space is married to real space through an equivalence relation which requires that the two observation methods agree on the result of a common event. For each fundamental constant the equivalence relation has a specific solution set. It contains the coding pattern for combining the individual harmonics for equivalence. Each combination establishes a specific harmonic mode.

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*Modal Harmonics and the Coding Patterns of Nature* (3/10/2014)

Cover : Abstract

Part 0: Introduction

Part I :

Part II: The Euler Equation

Part III:

Part IV: π

Part V: Conclusion

Part VI: Application-The Fibonacci Numbers

Part 0: Introduction

Part I :

*e*Part II: The Euler Equation

Part III:

*π*Part IV: π

^{2}Part V: Conclusion

Part VI: Application-The Fibonacci Numbers

### A Solution to the Reimann Hypothesis(9/9/2014)

**Simplifications & Corrections to the Pi Harmonics (10/27/2014)****Prime Number Table Formula (5/20/2015)**

### Casey’s Curves 24″ x 36″ Posters

- Abstract for Sheets 1 & 2 (4/19/2016)
- Sheet 1 –
*e*, π & natural log (4/22/2016) - Sheet 2 – Fibonacci Series, Golden Triangle & π
^{2}(5/2/2016) - Sheet 3 – π
^{3}& Summary of Some of the Simple Harmonics (7/6/2018) - Sheet 3.1 – Summary of Some of the Simple Harmonics (cont’d) (7/16/2018)

Free hard copies are available upon request.