Skip to content
JCSBimp's Hexagonal Orthogonal

JCSBimp's Hexagonal Orthogonal

BEWARE: There Be Fearfful Symmetries Here!

  • About J. Calvin “Bimp” Smith
  • Blog
  • Home
  • J. Calvin “Bimp” Smith’s Blog
  • Integer Factorization: Math Graphs du Jour

    Advertisements These are graphs of the behavior of the terms of the Series of Ceiling Roots for m=11882081 starting with the basic Ceiling Root of 3449 and increasing by 2. (See past posts for explanation and discussion of Ceiling Roots.) This is the crazy sort of pattern of numbers I hope to tame and characterize, […]

    JCSBimp

    February 1, 2023
    My Math Studies
    integer factorization, mathematical visualization, mathematics, number theory
  • Integer Factorization: Today’s Question

    Advertisements Consider an odd positive integer m for which one is seeking factorization. Consider the more or less typical case where the Ascent of the Ceiling Square of m is large, is turning out to be in the thousands or more; that is, a value of m for which the iterations of my Fermat-based factorization […]

    JCSBimp

    January 26, 2023
    My Math Studies
    fourier transform, integer factorization, mathematics, number theory, signal processing
  • Today’s Activism Post

    Advertisements Please consider signing my latest Resistbot petition. And also consider donating to Resistbot.

    JCSBimp

    January 25, 2023
    Political
    corporate personhood, politics
  • Integer Factorization: A 1313 Postscript, and the Next Example

    Advertisements I generated the Series of Ceiling Squares systematically for each Ascent associated with yesterday’s example of m=1313. I also assembled the Beehive Plot, but won’t include that here, except to say that when the hive’s slope increased linearly, the bee line was a nice parabola. Let’s do another one, slightly larger, where the factorization […]

    JCSBimp

    January 24, 2023
    My Math Studies
    integer factorization, mathematics, number theory
  • Integer Factorization: Let’s work an example.

    Advertisements Let m=1313. The square root of m is between 36 and 37. (m+1)/2 is odd, and so the ceiling root and square should be odd as well. c=37 already is. m is c squared minus 56, between 49 and 64. If we then let c ascend to 39, m is c squared minus 208, […]

    JCSBimp

    January 23, 2023
    My Math Studies
    integer factorization, mathematics, number theory
  • Integer Factorization: 18 Jan 2023 Update

    Advertisements I am currently examining my table of odd composite numbers that I have used for the 3D graph and the charts I shared a day or two ago, sorted according to remainder, and at the distribution and factors of the odd composite numbers for each such remainder. This was what led me to notice […]

    JCSBimp

    January 18, 2023
    My Math Studies
    integer factorization, mathematics, number theory
  • Integer Factorization: A Ceiling Square Tidbit

    Advertisements When one subtracts an odd positive integer m from its appropriately adjusted Ceiling Square c2, with the adjustment being made by adding 1 to ceil(sqrt(m)) if necessary to make it even or odd as (m+1)/2 is even or odd, respectively, the remainder r obtained by c2-m (so that m=c2-r) is always congruent to 0 […]

    JCSBimp

    January 17, 2023
    My Math Studies
    integer factorization, mathematics, number theory
  • Integer Factorization: New Charts

    Advertisements These charts are from my Numbers file for a recent study of Ceiling Squares, Remainders, and Ascents for the odd integers 1 through 999, with definitions of the quantities indicated as follows: If m is a positive non-prime integer: Let c be the integer ceiling of the square root of m. Adjust the value […]

    JCSBimp

    January 16, 2023
    My Math Studies
    integer factorization, mathematical visualization, mathematics, number theory
  • Integer Factorization: Series of Ceiling Squares, Take 3 (or 4)

    Advertisements I embarrassed myself twice this week, having to take down insufficiently debugged algorithms and Perl code for not testing thoroughly enough. However, I now have an algorithm I’ve once again tested, and will test some more (yes, opening the possibility that a bug will require me to correct/retract), and this one has a symmetric […]

    JCSBimp

    January 15, 2023
    My Math Studies
    integer factorization, mathematics, number theory, perl, Programming
  • Integer Factorization: Drop back and punt.

    Advertisements I had to backtrack and delete it post a couple of days ago, sharing my system for calculating Series of Ceiling Squares. It was not that the program was coded improperly, but rather that the algorithm’s math did not get rid of the “infinite telescoping” of the series for some value or another. I […]

    JCSBimp

    January 14, 2023
    My Math Studies
    integer factorization, mathematics, number theory
1 2 3 … 22
Next Page

Blog at WordPress.com.

  • About J. Calvin “Bimp” Smith
  • Blog
  • Home
  • J. Calvin “Bimp” Smith’s Blog