Tag: mathematical visualization

Danse Mathématique
Advertisements In which a representation of pairs of Azarya’s Angels (each pair a single dot) dance La Estrella del Mar through the eye of a needle, or the head of a pin, depending on one’s spatial apprehension.

My Integer Factorization Study: It’s Yrev, Very Good to See You Again, Old Friend.
Advertisements I decided to look at differences of squares near the values of numbers I wished to factor tonight. I took a particular randomlygenerated semiprime m, and started generating differences of squares, sequentially, that would come out near m. The first graph I observed showed a triangle of fairly randomly distributed dots. But then I […]

My Integer Factorization Study: The Hard Problem Remains
Advertisements Of course the hard problem of integer factorization remains! Should I succeed where so many others, with so many more well developed analytical tools have failed? And yet, I press on. In short, this is . . . The Hard Problem, in a(n Impenetrable) Nutshell Ceiling squares have gotten me a nice little efficient […]

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 […]

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 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 […]

Math Study: Number Pegboards and Series of Ceiling Squares
Advertisements I have put a new mathematical study paper up on Google Docs. This is my “Eureka” moment, even though I feel like I have been having a continuing series of those lately. (Is this what enlightenment feels and acts like?) To Ms. Rebecca Newberger Goldstein (https://twitter.com/platobooktour): Remember your character Azarya in “36 Arguments for […]

I Thank You All Very Much
Advertisements Now that inspiration that has been flooding into me in the form of my latest Number Pegboard mathematical study is starting to bear fruit in terms of its ideas and how to understand and communicate them, I am feeling very thankful. This mathematical study, along with all the others over the past couple of […]

Ceiling Squares: Final Paper Is Up, on Google Docs
Advertisements Below is a link to the more or less official description of a very, very intense, enlightening, and enjoyable mathematical study I have just completed, and it includes software for those who might wish to run Perl routines to illustrate some of the ideas I explored. https://docs.google.com/document/d/1or9NQfCKM11MhOoZ_nXe0G8uuVLIyeUpPalve9yuveg/edit?usp=sharing