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Textbook in PDF format

The first edition, an integration of my findings with the oriental concepts of Yin and Yang, was limited to 100 copies, and was privately distributed to an academic conference in Tokyo, 2005.
The second edition, entitled The Secret World of Numbers: New Discoveries in Mathematics, finished in 2011, was self-published for the general public on www.lulu.com. The comparisons with oriental thought were deleted in this expanded version.
The current, third expanded version, with the new title, was finished in the spring of 2020 and includes new and revised material. A brand new chapter entitled “Finding elements of so-called “irrational” square root sequences in constants hidden in reciprocals of rational numbers: a case of infinitely developing integers” has been added, while discussions about the Fibonacci numbers in light of a new analysis have been devoted to a separate, much expanded, chapter. The material on the numbers involved in our solar system has also been given its own much expanded chapter.
In the future I hope to add a chapter with my particular methodological analysis applied to geometry, which is also a branch of mathematics, as well as attempt to do so employing a biological model.
Furthermore, the entire question whether so-called irrational numbers may still yield a rational substructure remains an ongoing quest