On 2/26/2020 11:14 AM, ToddAndMargo via perl6-users wrote:
I used gnome calculator to 20 digits:
665857/470832
1.41421356237468991063
Sorry. Not seeing any repeating patterns.
Here is NAS doing it to 1 million digits (they have too
much time on their hands):
https://apod.nasa.gov/htmltest/gifcity/sqrt2.1mil
No repeats.
As well there shouldn't be in an irrational number. sqrt(2) !=
665857/470832
So why does base-repeating tell me there is a repeating
pattern when there is not?
Ah ha, 99/70 does have a repeat:
1.4142857 142857 142857 1
Maybe 665857/470832 I just do not go out enough digits to
see a repeat.
Correct. As a really disgustingly quick and dirty way of proving that
the expansion has a repeating cycle of 576 digits:
$ perl6 -e 'say
6658570000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/470832'
| perl -lne '/(\d{4,})\1/ and print length $1, ": $1"'
576:
135623746899106262955788901349101165596221157440445849050192000543718353892683589900431576443402317599483467563801950589594590002378767798280490705814388146939885139497740170591633533829476331260407109117477146837937948142861997485302613246338396710503958949264281102388962517415978523125021238998198932952730485608454820403031229822951711013694906038671967920617120331668195874536989839263261630475413735684915213919189859652699901451048356951099330546776769633329935093621504060896455635980562068848336561661059571142148367145818466034594080266421993407414959051211472457267
