Tag: mathematics

Math Stuff: The Tree of Eratosthenes?
Advertisements If we could see or build the Sieve of Eratosthenes the way a tree grows, from the bottom up, we might have no doubt, and much greater understanding, of its beauty and of the structure of the prime numbers. But its roots extend infinitely down, its branches growing up and up, and we cannot…

My Latest Math Study: Series of Ceiling and Floor Squares
Advertisements Ooh, I have a new mathematical obsession, following, as the last several such have done, from what I have just brought to some state of (in)completion. Consider the ceiling square of a positive integer m, the integer ceiling of the square root of m. Subtracting m from this number produces a remainder r. Applying…

AfterMath: Even Numbers Are Just Odd.
Advertisements The thoughts I still get in the early morning hours about numbers and factorization are not so imperative now that I have programmed and published that new, simple algorithm. Sometimes I can just smile at them and go back to sleep. And other times … they’re just WEIRD. This morning’s stayawakeandthinkaboutit notions concerned the…

The Presented Order of the Book of Thoth, and the Finite Field GF(79) – Part I, Introduction and Explanation
Advertisements This is a “mathemagical” discussion of the Book of Thoth, which is the collection of cards also commonly called the Tarot of the Egyptians, and how the symbolic order in which Aleister Crowley presented the 78 cards of that deck relates to certain arrangements – corresponding to the generators – of the elements of…

Factorization Perl Script Update
Advertisements I cleaned up the code for cf_exam.pl just now. Making the script better also made it a little shorter, but I doubt that it is any faster. Anyway, have at it!

Integer Factorization: A New and Very Simple Script
Advertisements A little over a month’s worth of mathematical and numerical study and effort, ending in an amazing week of realization about the structure of numbers and their factors, have led me to a finished product which, despite probably not being revolutionary, leaves me feeling very satisfied about what I have learned, and all the…

Some Number Theory
Advertisements Let prime number p be a factor of positive integer m. The integer m has an expression as the difference between two perfect squares s and t, with s greater than t, such that either s+t or st equals p. When m=p×1, this will be the only such s and t, and s=t+1. Define…

Math Insight, After a Morning “Off”
Advertisements Early Tuesday morning, I popped awake, but no mathematical insight was waiting to compel me to stay awake. However, i did walk quietly downstairs to work on my mathematical study, as I have been doing every early morning since the insights started coming – about a week and change now, I think. I took…

This Morning’s Math Realization
Advertisements Azarya’s Angels did not give me a realization as the result of a train of thought that seized me upon popping awake very early. However, I did pop awake early, and began studying data while enjoying coffee and a donut, and by about 7 a.m., the realization for which the Angels apparently awakened me…

Math Study Progress
Advertisements I have added all the information I have figured out so far about splitting roots and ceiling discrepancy, as well as the colorful chart I shared here earlier, to the report on Telescoping the Integers. (link) So far, it contains nothing suggestive of new advances in integer factorization, but time and further study will…