Category: My Math Studies

Laura P. On Studying Ascents
Advertisements I feel like I’m going to dream tonight. Big, bad ones. You know, the kind you like? [excerpt from Twin Peaks season 1 episode 7]

The Ascent of m: A Concept Whose Properties I Shall Explore Soon
Advertisements The minuend of any such squaredifference expression of m will then be greater than m’s ceiling square. Define the ascent of such a factorization or corresponding squaredifference expression as the difference between the square root of the minuend in that expression and the ceiling root of m. EXAMPLES: The ascent of the trivial factorization…

Another Excerpt from “Ceiling Squares, Central Squares, and Factorization”
Advertisements Now consider an arbitrary odd positive integer m, its trivial factorization as 1*m, and its corresponding expression as the difference of two squares [(m+1)/2]2[(m1)/2]2. Since m is odd, either the minuend (the first term) is even and the subtrahend (the second term) is odd, or vice versa, as follows: When m is congruent to…

Slightly Upset Stomach, Disconcerting Dream
Advertisements Tummy wasn’t just exactly right this morning, and so… I dreamed I was on Wilmington Island, between Savannah and Tybee, and I had discovered a shocking result of my mathematical studies: Numbers were controlling human beings! Everyone had a number, it was programmed into us somehow, each was different, and there were two different…

Math: An Excerpt from InProgress Report
Advertisements Ceiling Squares and Discrete Semiprimes A discrete semiprime is the product of two distinct prime numbers. A discrete semiprime has exactly four divisors. If m=ab is a semiprime, with a and b the prime factors of m, and ordered so that a<b, then m has exactly four divisors which are, in numerical order: 1,…

Wed Jun 8 3:43 AM – MIRIAM wakes me with a Vision
Advertisements Yes, dear reader, it was bound to happen sometime, I guess! I slept soundly, having gone up to the bedroom before my wife got sleepy, and the dogs came up to settle in with me, too. And I slept, and I dreamed, and it had to do with ceiling squares and integer factorization, but…

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…

Her Name Is MIRIAM.
Advertisements The inspiration that wakes me up early with rapidfire thoughts and ideas, usually mathematical in nature, now has a name. I have decided to call that inspiration, or angel, or muse MIRIAM: Moving Ideas Rapidly Into Accepting Minds. The name, it turns out, is a feminine Hebrew name for “A Star of the Sea,”…

The Mathematical Tree Up Which I Am Barking Now (June, 2022)
Advertisements It’s the same old tree as before, pretty much, but hey… When m is any odd positive integer, choosing a=1 and b=m gives a factorization of m into ab. In this case, the perfect squares of the appropriate range whose difference gives the equation m=ab come from observing that solving the system of equations…

Cute Li’l Number
Advertisements In building my current math study tables – from which the graphs in the previous post came – I encountered the number 385, which, as a direct consequence of its factoring into two factors in exactly four different ways, also has four different expressions as the difference of two squares. This in itself is…