Divisor Drips and Square Root Waves
by Jeffrey Ventrella

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Table of Contents
1. A Pattern-finding Journey
2. Divisor Drips and Reflection Rays
3. The Square Root Spine
4. Fantabulous Parabolas
5. Resonating Waves
6. Relation to the Number Spiral
7. Many Divisors, Many Paths
8. Emergent Patterns
9. A New Appreciation of Number
10. References
11. Acknowledgements


References

[1] Chaitin, G. Meta Math! The Quest for Omega. Pantheon. 2005 page 16

[2] Cox, D. Visualizing The Sieve of Eratosthenes. Notices of the American Mathematical Society. volume 55, issue 5, page 579. 2008

[3] du Sautoy, M. The Music of the Primes. Harper Collins, 2003. Page 34

[4] Kirk, A. Catching Primes. +Plus Magazine, Issue 47, 2008. University of Cambridge Millennium Mathematics Project Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA. Website: http://plus.maths.org/content/catching-primes

[5] Lakoff, G. and Nuñez. R. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic. 2000

[6] Riemann, B. "On the Number of Primes Less than a Given Magnitude". In Gesammelte Werke, Teubner, Leipzig. 1859.

[7] Rucker, R. Mind Tools - the Five Levels of Mathematical Reality. Houghton Mifflin Company, 1987.

[8] Sabbagh, K. quoted in the book, What We Believe but Cannot Prove. Ed. Brockman, J. Harper Perennial, 2006. page 21

[9] Sacks, R. Number Spiral. 2003. web site published online at: http://www.numberspiral.com/ 2003 - 2007 by Robert Sacks

[10] Stein, M. L., S. M. Ulam, and M. B. Wells. 1964, A visual display of some properties of the distribution of primes. AMA 71(May):516-520.

[11] Thomasson, D., From Knight Moves to Primes. 2001. web site published at http://www.BordersChess.org/KTprimes.htm 2001 by Dan Thomasson

[12] Tomes, R. Harmonics Theory - The Physics and Maths: web site address: http://ray.tomes.biz/maths.html

[13] Ventrella, J. Prime Numbers are the Holes Behind Complex Composite Patterns. Presented at the International Conference on Complex Systems 2007, October 28-November 2, Boston, MA. web site: http://knowledgetoday.org/wiki/index.php/ICCS07/240

[14] Wolfram, S. 2002. A New Kind of Science. Wolfram Media, Inc. page 132

11. Acknowledgements


Table of Contents
1. A Pattern-finding Journey
2. Divisor Drips and Reflection Rays
3. The Square Root Spine
4. Fantabulous Parabolas
5. Resonating Waves
6. Relation to the Number Spiral
7. Many Divisors, Many Paths
8. Emergent Patterns
9. A New Appreciation of Number
10. References
11. Acknowledgements