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The Remarkable Number 1/89 (2004)

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Re: The Remarkable Number 1/89 (2004)

#41

Post by cleansingfire »

doodpants wrote: post #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.

This seems like a pretty basic calculus problem. Constants become irrelevant at the limit, so that the relationship (ratio) is all that's left.

Re: The Remarkable Number 1/89 (2004)

#43

Post by whatshisface »

Cullinet wrote: post #29
ckemere wrote: post #17

Presumably in a different number base, the number would be different. Would it still be in the aeries?

Without any basis whatsoever, and I really must one day put this idea out of its misery with some studying, I long suspected that quantum mechanics involved parallel universes where different bases more aptly fit with that other reality. My thought is surely crackpot but I'll explain how my idea arose : A fraction eg 1/3 describes a decimal number to infinite accuracy but creates a challenge for base 10 calculations.…

Base 10 doesn't fit particularly well with our reality, it was picked for historical reasons. Every other base works just as well.

Re: The Remarkable Number 1/89 (2004)

#44

Post by red_phone »

NickHoff wrote: post #39
chrismorgan wrote: post #34

On the decimal expansion part, 1⁄7 has always fascinated me, having something very similar going on. Doubling from 7, you get 14, 28, 56; and 1⁄7 is 0.1̅4̅2̅8̅5̅7̅, 2⁄7 is 0.2̅8̅5̅7̅1̅4̅, 3⁄7 is 0.4̅2̅8̅5̅7̅1̅, &c. (just changing which digit you start the recurring sequence with). https://en.wikipedia.org/wiki/142,857 talks about it a bit more; the doubling sequence thing is covered in the section 1⁄7 as an infinite…

I've always liked 1/7 as well, and I never realized that thing about doubling from 7 giving 14, 28, 56. People are always impressed when I can rattle off the digits of x/7. By the way, I appreciate your use of U+0305 combining overline. Did you enter those manually or do you have some neat way of doing it?

To me, the fact that you’re in an environment where knowing the digits of x/7 is appreciated is the most-impressive thing of all!

Re: The Remarkable Number 1/89 (2004)

#47

Post by kazinator »

alisonkisk wrote: post #23
wumms wrote: post #11

From an archived talk (2011) on wikipedia [0]: "The linked page misleadingly suggests that a certain Cody Birsner discovered the relationship between the series and the fraction, whereas it had been known for a considerable time before". Günter Köhler, 1983 (published in the The Fibonacci Quarterly, 1985; who cites earlier papers from 1977 and 1981): https://www.fq.math.ca/Scanned/23-1/kohler.pdf [0] https://en.wikip…

It's a bit silly to chase down original authorship of an idea that is a minor detail visible to many people who work in a field. It's like asking who was the first person to discover that all multiples of 11 have the same parity in the respective sums of their odd and even digits.

Since there had to be a first person who discovered that all multiples of 11 have the same parity in the respective sums of their odd and even digits, that question is obviously interesting to some historians. Due to what circumstances was that person first? What hindered others before that person? How long was the lag before use of decimal and the discovery?

Re: The Remarkable Number 1/89 (2004)

#48

Post by prezjordan »

alisonkisk wrote: post #26
burlesona wrote: post #2

Okay, 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 ?

You might also enjoy tan(1 degree/55555555555)

Fun video about this one on Numberphile https://www.youtube.com/watch?v=IMY2_yzDm9I

Re: The Remarkable Number 1/89 (2004)

#49

Post by chrismorgan »

NickHoff wrote: post #39
chrismorgan wrote: post #34

On the decimal expansion part, 1⁄7 has always fascinated me, having something very similar going on. Doubling from 7, you get 14, 28, 56; and 1⁄7 is 0.1̅4̅2̅8̅5̅7̅, 2⁄7 is 0.2̅8̅5̅7̅1̅4̅, 3⁄7 is 0.4̅2̅8̅5̅7̅1̅, &c. (just changing which digit you start the recurring sequence with). https://en.wikipedia.org/wiki/142,857 talks about it a bit more; the doubling sequence thing is covered in the section 1⁄7 as an infinite…

I've always liked 1/7 as well, and I never realized that thing about doubling from 7 giving 14, 28, 56. People are always impressed when I can rattle off the digits of x/7. By the way, I appreciate your use of U+0305 combining overline. Did you enter those manually or do you have some neat way of doing it?

Heh, last time I spouted about 1⁄7 here someone asked about the overline too: https://news.ycombinator.com/item?id=24302104. I love my Compose key.

Re: The Remarkable Number 1/89 (2004)

#50

Post by zekrioca »

alisonkisk wrote: post #23
wumms wrote: post #11

From an archived talk (2011) on wikipedia [0]: "The linked page misleadingly suggests that a certain Cody Birsner discovered the relationship between the series and the fraction, whereas it had been known for a considerable time before". Günter Köhler, 1983 (published in the The Fibonacci Quarterly, 1985; who cites earlier papers from 1977 and 1981): https://www.fq.math.ca/Scanned/23-1/kohler.pdf [0] https://en.wikip…

It's a bit silly to chase down original authorship of an idea that is a minor detail visible to many people who work in a field. It's like asking who was the first person to discover that all multiples of 11 have the same parity in the respective sums of their odd and even digits.

Then it is also silly to (erroneously) mention who discovered such a property, don't you think?
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