71–80 of 120 posts
this reminds me of the online encyclopedia of integer sequences ( https://oeis.org/ ). anything similar for things like 987654321 / 123456789 ?
but i still wonder if there is something like OEIS for observations / analysis like this
I like calculator quirks like this. I remember as a kid playing with the number pad and noticing a geometric center of mass in number sequences ┌───┬───┬───┐ │ 7 │ 8 │ 9 │ ├───┼───┼───┤ │ 4 │ 5 │ 6 │ ├───┼───┼───┤ │ 1 │ 2 │ 3 │ ├───┼───┼───┤ │ 0 │ . │ │ └───┴───┴───┘ I remember seeing that (14787 + 36989) / 2 would produce 25888, in that the mean of geometric shape traced by the two sequences would average out in the…
i remember the 1110 thing on a calc as well. 741 + 369 & 963 + 147 | 123 + 987 & 321 + 789 (left right | up down) 159 + 951 & 753 + 357 | 258 + 852 & 456 + 654 (diagonally | center lines) the design of a keypad... it unintentionally contains these elegant mathematical relationships. i call this phenomena: outcomes of human creations can be "funny and odd", and everybody understand that eventually there will be always…
I like calculator quirks like this. I remember as a kid playing with the number pad and noticing a geometric center of mass in number sequences ┌───┬───┬───┐ │ 7 │ 8 │ 9 │ ├───┼───┼───┤ │ 4 │ 5 │ 6 │ ├───┼───┼───┤ │ 1 │ 2 │ 3 │ ├───┼───┼───┤ │ 0 │ . │ │ └───┴───┴───┘ I remember seeing that (14787 + 36989) / 2 would produce 25888, in that the mean of geometric shape traced by the two sequences would average out in the…
The even simpler example is more striking imo. (147 + 369) / 2 = 258 and (741 + 963) / 2 = 852
I like calculator quirks like this. I remember as a kid playing with the number pad and noticing a geometric center of mass in number sequences ┌───┬───┬───┐ │ 7 │ 8 │ 9 │ ├───┼───┼───┤ │ 4 │ 5 │ 6 │ ├───┼───┼───┤ │ 1 │ 2 │ 3 │ ├───┼───┼───┤ │ 0 │ . │ │ └───┴───┴───┘ I remember seeing that (14787 + 36989) / 2 would produce 25888, in that the mean of geometric shape traced by the two sequences would average out in the…
The even simpler example is more striking imo. (147 + 369) / 2 = 258 and (741 + 963) / 2 = 852
(741 + 963)/2 = (700+900)/2 + (40+60)/2 + (1+3)/2, it's just average in each decimal place.
this reminds me of the online encyclopedia of integer sequences ( https://oeis.org/ ). anything similar for things like 987654321 / 123456789 ?
...followup after looking through comments on OP, indeed someone else already had the idea to tie in OEIS sequences in the comment at https://www.johndcook.com/blog/2025/10/26/987654321/#comment... but i still wonder if there is something like OEIS for observations / analysis like this
I like calculator quirks like this. I remember as a kid playing with the number pad and noticing a geometric center of mass in number sequences ┌───┬───┬───┐ │ 7 │ 8 │ 9 │ ├───┼───┼───┤ │ 4 │ 5 │ 6 │ ├───┼───┼───┤ │ 1 │ 2 │ 3 │ ├───┼───┼───┤ │ 0 │ . │ │ └───┴───┴───┘ I remember seeing that (14787 + 36989) / 2 would produce 25888, in that the mean of geometric shape traced by the two sequences would average out in the…
For non-Americans and/or those too young to remember when landline service was still dominant, in the 90s and early 2000s AT&T ran a collect-call service accessible through the number 1-800-CALL-ATT (1-800-225-5288) and promoted it with ads featuring comedian Carrot Top. And if you don't know who Carrot Top is, maybe that's for the best.
> The exact ratio is not 14, but it’s as close to 14 as a standard floating point number can be. How do you get around limitations like that in science?
> The exact ratio is not 14, but it’s as close to 14 as a standard floating point number can be. How do you get around limitations like that in science?
This was by far the most interesting part to me. I've never considered that code and proofs can be so complementary. It would be great if someone did this for all math proofs! "Why include a script rather than a proof? One reason is that the proof is straight-forward but tedious and the script is compact. A more general reason that I give computational demonstrations of theorems is that programs are complementary to…
This is misleading in that the (Curry–Howard) correspondence is between proofs and the static typing of programs. A bug in a proof therefore corresponds to a bug in the static typing of a program (or to the type system of the programming language being unsound), not to any other program bug. (Also: complementary != complimentary.)
a) it can be actually helpful to check that some property holds up to one zillion, even though it's not a proof that it holds for all numbers; and
b) if a proof has a bug, a program checking the relevant property up to one zillion is not unlikely to produce a counterexample.
This was by far the most interesting part to me. I've never considered that code and proofs can be so complementary. It would be great if someone did this for all math proofs! "Why include a script rather than a proof? One reason is that the proof is straight-forward but tedious and the script is compact. A more general reason that I give computational demonstrations of theorems is that programs are complementary to…
What I was actually good, or at least fast at, was TI-Basic, which was allowed in a lot of cases (though not all). Usually the problems were set up so you couldn’t find the solution using just the calculator, but if you had a couple of ideas and needed to choose between them you could sometimes cross off the wrong ones with a program.
The script the author gives isn’t a proof itself, unless the proposition is false, in which case a counter example always makes a great proof :p