Category: My Math Studies

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…

Curious Hieroglyphics
Advertisements … which our intrepid blogger has found inscribed on the positive odd integers.

Mathematical Insights, an Update: Ceiling Squares and Central Squares
Advertisements But First: A Very Personal Psychological/Spiritual/Mystical/IReallyDon’tKnowWhatExactlyItIs Side Trip My mathematical insights are still coming fairly predictably almost every night, trains of thought that feel inspired and that push me to think them to completion, or at least to some kind of form. My Primary Care Physician sees my state as being similar to that…

Because I’m Doing It All Wrong! 😀 [copied from Facebook]
Advertisements The conversation I have in my head when I wake up most of these early mornings, take care of the dogs’ needs, and then can’t get to sleep because I am thinking about [censored]*, goes kind of like this (and I’m tickled that it’s another Kevin Smith George Carlin reference): ME: What am I…

My Math Mind: Mistaking the Pedestrian for the Profound Since, er, Coupla Months Ago, Maybe?
Advertisements I keep getting these insights that make me go “Wow!” and then two seconds later, or sometimes two days later, depending on the complexity of the idea in question, I go “Waitaminnit… that’s not really profound at all. It’s closer to pedestrian, and almost PROFANE.” Okay, I don’t go that in so many words.…

Math Stuff: The Tree of Eratosthenes?
Advertisements If we could see or build the Sieve of Eratosthenes the way a tree grows, from the bottom up, we might have no doubt, and much greater understanding, of its beauty and of the structure of the prime numbers. But its roots extend infinitely down, its branches growing up and up, and we cannot…

My Latest Math Study: Series of Ceiling and Floor Squares
Advertisements Ooh, I have a new mathematical obsession, following, as the last several such have done, from what I have just brought to some state of (in)completion. Consider the ceiling square of a positive integer m, the integer ceiling of the square root of m. Subtracting m from this number produces a remainder r. Applying…

AfterMath: Even Numbers Are Just Odd.
Advertisements The thoughts I still get in the early morning hours about numbers and factorization are not so imperative now that I have programmed and published that new, simple algorithm. Sometimes I can just smile at them and go back to sleep. And other times … they’re just WEIRD. This morning’s stayawakeandthinkaboutit notions concerned the…

Factorization Perl Script Update
Advertisements I cleaned up the code for cf_exam.pl just now. Making the script better also made it a little shorter, but I doubt that it is any faster. Anyway, have at it!