almost immediately after posting about using gppf as a measure of roundness, another one of course crossed my mind. i've been calling it IFR, for Inner Factor Ratio. by "inner factor"(s), i mean the two factors closest to the number's square root. so, for instance, the factors of 12 are 1, 2, 3, 4, 6, 12. the two numbers closest to its square root ( Read more... )

because i never really stop thinking about anything, i'm going to again go on for a little bit about quantifying the roundness of numbers. way back here, i mused about looking at the greatest prime factor gpf(n) of an integer, and defining an integer's roundness as logngpf(n). at the time, i commented:the problem with this method is that it tends ( Read more... )

both π day and the more recent τ day (both more recent = it was yesterday and more recent = it hasn't been celebrated for as many years) suffer from the same problem: they depend on the decimal expansion of one or t'other of the circle constants. using base 10 is precisely the sort of arbitrary choice that going to radian measure of angles is ( Read more... )

jugglingstore, mian1wzd, neverexost, and renegadesufi, i'm curious about how you came to friend me on LJ. where did you find my journal? you realize that, as per my friending policy, discussed on my profile page, i'm not gonna be friending you back any time soon. right ( Read more... )

ever since first seeing walken dance his way through the video for Fat Boy Slim's Weapon of Choice it's been obvious to me that the song needed a mathematical filking. thus, i present

Axiom of Choice

Don't be shocked by Cohen's and Gödel's voice
Check out my new axiom, axiom of choiceDon't be shocked by Cohen's and Gödel's voice ( Read more... )

on a walk the other day, i noticed that several of the passing (three-digit) license plate numbers i factored ended up having a greatest prime factor (gpf) of 31. as in, i think, four in six consecutive plates. of course, i wondered if there was anything to that. as the largest three-digit number is 999 (roughly 1000), and the square root of 1000 ( Read more... )

( cut for do you really care? )

why is it that the african nation called the gambia is called "the gambia" instead of just "gambia"? i recognize that articles on country names are common in other languages. auf franzözisch, zum beispiel, man sagt "le canada", aber auf englisch man sagt nicht "the canada". i remember that we used to call ukraine "the ukraine", but that stopped ( Read more... )

i continue to think about roundness quantification when i've got nothing better to do. another approach, one might even say a classic approach, would be to ask how many numbers smaller than n share factors with n. if there are lots of them, n is round. not so many, not so round ( Read more... )

( silly but not cut for that. cut for statistics and mild-to-moderate BSG spoilers. )