JCSBimp's Hexagonal Orthogonal

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=c2-m, we can construct a Zone Grid and compute the slope of a Remainder Line passing through appropriately chosen values of r0=r and…

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 almost-year. I wrote the Perl script for the Initial Trapezoid I talked…

Advertisements Not all of the work is done yet, and the thought-work 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,…

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…

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 two-dimensional travel path taken by successive remainders c2-m, (c+1)2-m, … (c+n)2-m, … where m is the odd…

Advertisements By J. Calvin Smith, B.A., Mathematics, Georgia College, Milledgeville, Georgia, United States of America (1979) – Retired Member, American Mathematical Society Written 14 March 2023 at Mountain River Chalet (the author’s home), Talking Rock, Georgia, USA. The following definitions, theorem, and construction are the end result of research by the author into factorization of…