The Remarkable Number 1/89 (2004)
www2.math.ou.edu
The Remarkable Number 1/89 (2004)
1–10 of 116 posts
Re: The Remarkable Number 1/89 (2004)
#2Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?”
But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why?
Re: The Remarkable Number 1/89 (2004)
#3Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?” But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why ?
[deleted]
Re: The Remarkable Number 1/89 (2004)
#4"The successive ratios of the terms, i.e. 1/1, 2/1, 3/2, 5/3 ... tend to a number called the Golden Ratio by the Greeks."
Fun fact: take any two numbers (e.g. chosen randomly), and use them as the seeds for a Fibonacci-like sequence by summing the last two terms to generate the next term. The ratio of any two consecutive terms in that series will tend towards the golden ratio.
Re: The Remarkable Number 1/89 (2004)
#51/89 = .01123595505..., not .01123595595..., small typo
Re: The Remarkable Number 1/89 (2004)
#6> As you can easily check, 1/89 = .01123595595... Bizarre, eh?
Typo: 1/89 = .01123595505...
Re: The Remarkable Number 1/89 (2004)
#7Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?” But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why ?
In addition to this question I would like to know if you can in general say/proof that for every sequence which has some relation between the successive numbers there is a rational number whose decimal expansion is the same as the sequence.
Re: The Remarkable Number 1/89 (2004)
#8Any number is remarkable if you're smart enough to find why it's remarkable.
Re: The Remarkable Number 1/89 (2004)
#9Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?” But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why ?
There's a "theorem" about this:
> The interesting number paradox is a semi-humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction.
Re: The Remarkable Number 1/89 (2004)
#10Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?” But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why ?
In addition to this question I would like to know if you can in general say/proof that for every sequence which has some relation between the successive numbers there is a rational number whose decimal expansion is the same as the sequence.
A standard technique to find explicit expressions for the `n`th number of a recursion is through generation functions; see e.g. https://en.wikipedia.org/wiki/Generating_function. You can plugin x = 10^-1 there. Not sure if the result is always a rational number.