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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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

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

**Simplifications & Corrections to the Pi Harmonics (10/27/2014)****Prime Number Table Formula (5/20/2015)****Casey’s Curves (4/18/2016)**