I was bored and typed sqrt(546) into wolfram and made it show as many digits as it was capable of. How come there are so many strings of repeating numbers? Dubs, trips, hell even some quads. Didn't look very hard so I don't know if there are any quints.
Why not? Suppose that every digit appears randomly. Then caluclate the probability of appearing dubs, trips, hell even some quads.
Brody Cruz
Its probable that the program works on some sort of a sequence to generate randome numbers. And after the sequence is done it kinda starts repeating itself
Robert Williams
>Suppose that every digit appears randomly
Not all irrational number are normal
Logan Myers
He didn't say it was a matter of fact, he said "suppose" as working hypothesis
Why would you even think to search it though, if you didn't already know it was related to ponies?
Chase Butler
idk i just fucking searched it dude
Tyler Sanders
Just tested it with the first 99960 digits of sqrt(546) 10026 dubs 1010 trips 97 quads
which are all in good agreement with the theoretical expectation (9996, 1000, 100).
Aaron Anderson
>1000, 100 999.6, 99.96 surely?
Chase Sullivan
>hell even some quads
Given any sequence of 4 digits, the odds that the 2nd, 3rd, and 4th are the same as the 1st is 1/10 x 1/10 x 1/10 = 1/1000. So every thousandth set of 4 digits will be a quad, on average. You have, what, 2500 digits there? Somewhere close to that. So there should be 2 or 3 quads there, along with about 25 trips and 250 dubs.
Jaxon Brooks
Oh, but then there's the fact that every individual digit could be the start of a 4 digit sequence, so there'll be more quads than that.
Kayden Evans
question:
are there ALGEBRAIC nubers i.e. irrational numbers formed by square routes of rational numbers which have properties like e.g." no digit in base 10 of a^(1/b) is the digit 2 where a and b are both rational"
or similar properties that only make sense in base 10?
how would you go about proving hat there is no such algebraic number with those kinds of properties?
that for every pattern specific to base 10 you specify, like "this algebraic number only has the digit "2" when the power of 10 column is a multiple of 5" every algebraic number will eventually violate that pattern after enough digits
Xavier Morales
Actually 4569 digits after the decimal.
6 quads total.
Hunter Cooper
Well at least I can find one counterexample with a = 1 and b = 1, since 1 has no digit 2
For your second example you can have the number 0.000020000200002... which would be rational, and thus algebraic.
When you keep turning the same direction after n metres.
Parker Walker
kek
Angel Gutierrez
kek
Henry Bailey
kek
Brandon Miller
kek
Joshua Morales
I meant > irrational numbers formed by square roots(etc) of rational numbers which have properties like e.g." when expressed in base 10, no digit of a^(1/b) is the number "2" where a and b are both rational"
the examples you both gave are rational
Angel Smith
really, op? you have a thousand digits and expect no repeating number? that would mean a digit can't be the same as the one before it or the one next to it and there are only 10 digits.
Zachary Russell
dubs, trips, quads are integral to the fabric of reality