Category: My Math Studies

Integer Factorization: My Latest Findings, 30 March 2023
Advertisements “It’s amazing what a relatively lackluster Junior and Senior year in college math, followed by 33 years of working for the government bureaucracy, will do to one’s expectations of oneself in one’s major field. “I am actually startled, especially in retrospect, that I’m sitting here now, at age 65, working out new results, and…

Integer Factorization: The Gauntlet
Advertisements [userpic:jcsbimp] gets a feeling of determination, nay, almost a feeling of finality [userpic:jcsbimp] thinks of the past year and all he has learned, all the concepts he has developed in this mathematical study: the Ceiling Square, the Remainder, the characteristic polynomial, the Beehive Plot and the Bee Line, the Zone Grid and the Remainder…

Integer Factorization: Patterns in the Weeds
Advertisements When m is an odd positive integer, c2 is the least perfect square greater than or equal to m that is odd or even as (m+1)/2 is odd or even, and r=c2m, we can construct a Zone Grid and compute the slope of a Remainder Line passing through appropriately chosen values of r0=r and…

Integer Factorization: Deez Numbahs Iz Kwazy!
Advertisements Truly I find myself in the weeds here, folks. And that’s a good thing. It’s good because the process of getting myself out of the tangle of weeds could involve untangling the principal tangle with which I’ve concerned myself for this past almostyear. I wrote the Perl script for the Initial Trapezoid I talked…

Integer Factorization: The Initial Trapezoid
Advertisements Not all of the work is done yet, and the thoughtwork has just begun, but I wanted to update with a screenshot of the concept of the Initial Trapezoid: the quadrilateral bounded by the green and red lines where the Remainder Line in orange, passing through a typical pair of remainders r0 and r1,…

Integer Factorization: Playing With the Zones
Advertisements It occurred to me tonight to start looking at the successive remainders on the Zone Grid in a different way. During my studies of this arrangement of number lines vertically shifted by quadratic amounts on the Cartesian Plane, I discovered that a “skew” linear transformation of the zone lines and the Remainder Line preserves…

II seirtemmyS lufraeF
Advertisements Factor, factor, burning bright, In some wavelength beyond light, For you I seek, frustrated. Is all my work illfated?

Fearful Symmetries
Advertisements Sometimes, to look at fearful symmetries, I just need typeset graphics, if you please.

Integer Factorization: Update for 21 March 2023
Advertisements This update refers to concepts defined in earlier posts, without explaining them extensively here. I have placed links at the bottom of this post to recent explanatory posts. In designing my most recent approach, I produced a twodimensional travel path taken by successive remainders c2m, (c+1)2m, … (c+n)2m, … where m is the odd…