Tag: mathematics

Mathematical Thoughts: This Morning’s Gifts
Advertisements This morning’s gifts (which I could consider to be from the Queen of the Sciences Herself or from “Azarya’s Angels” who appear to serve as Her messengers to me), the mathematical insights it occurred to me in the early morning hours to ponder, relate to two concepts I have newly discovered: ceiling discrepancy and […]

New Math Paper in Progress
Advertisements The new report on Telescoping the Integers is in progress, and you can go see what’s there so far, if you wish. I shall be exploring and writing a good bit more on it as soon as tonight. https://docs.google.com/document/d/1jpcGfykv5sQl4OPAEx2k8On0oN17cmKGuCI_9xdUaqI/edit?usp=sharing

A New Math Study: Telescoping the Integers, and the Series of Ceiling Roots
Advertisements Yes, it appears mathematics is not done with giving me a flood of ideas in the early morning hours. This time, it was in the form of interesting observations, some of which I felt compelled to work out while I was trying to get back to sleep in preparation for my church choir job, […]

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 […]

A New Math Study: Numbers on a Pegboard
Advertisements For my latest mathematical explorations, the inspiration for which have come like the Ceiling Squares study in the form of ideas demanding me to pursue them in the early hours of morning, I have come up with a way to assign odd integer values to integer points on the Cartesian grid of x>0 and […]

Ceiling Squares: You Can Generalize, if You Wanna, but You Will Lose the Squareness
Advertisements I thought of, and actually fiddled with, a generalization of ceiling squares to include all positive integers, excluding perfect squares, both even and odd. Though not a genuine problem with this, there are some tradeoffs that make me say “Why bother?” For a given perfect square ceiling s2, there will now be 2s2 rows […]

The Latest Math Idea to Get Me Up Early
Advertisements All possible factorizations into two factors of the positive integers correspond to all integer points on the family of curves y=m/x, for m an element of the infinite set {1,2,3,4,5,…}, and we can restrict our attention, thanks to mirror symmetry, to the points where x and y are greater than zero (symmetric by Cartesian […]

Mathypiphanies: One in a Continuing Series (I Just Started)
Advertisements It now occurs to me that the Ceiling Squares are little more than square chunks cut out of the fabric of an oddinteger modulararithmetic version of the Sieve of Eratosthenes. Ya beautiful, Ceiling Squares, but ya basic. (With apologies for cultural lingo appropriation, however trendy.)

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