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[-] lauha@lemmy.world 165 points 6 months ago

This is because fibonacci numbers approach golden ratio which is approximately 1,618033... and one mile is 1,609344 kilometres exactly.

[-] Oisteink@lemmy.world 28 points 6 months ago
[-] lauha@lemmy.world 6 points 6 months ago
[-] 0_0j@lemmy.world 2 points 6 months ago
[-] gnawmon@ttrpg.network 31 points 6 months ago
[-] Landless2029@lemmy.world 13 points 6 months ago

And yet the military uses "clicks"

[-] gwl 3 points 6 months ago

0.54 nmi (nautical miles)

[-] ExperimentalGuy@programming.dev 20 points 6 months ago

This is such a cool example of how some recursive algorithms have a closed form. We all know that there's a simple equation to plug miles into to get kilometers, but we don't talk about how the Fibonacci sequence has a closed form. This is so cool.

[-] angrystego@lemmy.world 5 points 6 months ago

Wjat does closed form mean? Asking as a stupid botanist, sorry.

[-] WolfLink@sh.itjust.works 5 points 6 months ago* (last edited 6 months ago)

Closed form means it can be written out as a specific, finite set of instructions that work the same regardless of what the input to your function is.

For Fibonacci, it is most commonly defined in its recursive form:

f(0) = 0
f(1) = 1
f(x) = f(x-1) + f(x-2) for integer x > 1

But using this form, computing a very large Fibonacci number requires computing all the numbers before it, so it’s not the same finite set of instructions for every number, it takes more computation to generate larger numbers.

However, there is a closed form formula for generating Fibonacci numbers. Using this formula, you can directly compute any large Fibonacci number without having to compute all those intermediate steps. It takes the same amount of work to compute any Fibonacci number.

f(x) = (a^x - b^x)/√5
a = (1+√5)/2
b = (1-√5)/2

(Note that a and b here are constants; I only wrote them separately to avoid a mess of nested parenthesis)

For an example of something that doesn’t have a closed form, we do not know of a closed form for generating prime numbers. There are several known algorithms for generating the nth prime number, but they all depend on computing all the previous prime numbers, making it very difficult to compute very large prime numbers (in fact, how generating large primes is actually done is by making an educated guess and then checking that it’s actually prime). Discovering a closed form formula for prime numbers would have a huge impact on mathematics and cryptography.

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[-] ramble81@lemmy.zip 12 points 6 months ago

To go from km to mi I always leaned “multiply by 6 and move the decimal one to the left”. So 6km is ~3.6mi. Or 10km is just about 6mi.

[-] davidagain@lemmy.world 7 points 6 months ago

Yes. That uses the 3:5 ratio.

[-] pupbiru@aussie.zone 2 points 6 months ago* (last edited 6 months ago)

or add half and then 10% (because it’s 1.6km to the mile): easier than multiplying decimals or large numbers by 6, and the inverse is 0.6mi=1km so easy to remember both ways (same thing but don’t “add” just start from 0)

[-] Scavenger8294@feddit.org 1 points 6 months ago

glad I did not learn conversion in school. Nobody uses miles where i live

[-] untorquer@lemmy.world 1 points 6 months ago

I used to remember because space (Karman line) is 100km or 62mi up. I guess it helps to be a space nerd for that one. Kind of just figure 1.6 going the other way.

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[-] gwl 8 points 6 months ago* (last edited 6 months ago)

Ah yes, I always remember the Fibonacci sequence and totally wouldn't find it harder to calculate than just doing the conversion the regular way

/sarcasm

[-] Dumhuvud@programming.dev 5 points 6 months ago

"Remember"? Do you also remember all the digits of π?

It's defined as F(0) = 0, F(1) = 1 and F(n) = F(n - 1) + F(n - 2). Which makes more sense than imperial units.

[-] gwl 5 points 6 months ago* (last edited 6 months ago)

Or I could just do 1.6 km ≈ 1 mile whenever I need to convert from the standard that I use, Metric, to Imperial

Far far far simpler

Edit: I'm not American, I use sensible units, SI Metric

Edit edit: I do fully have dyscalcus, mostly only effects "scary" looking maths, so no, your suggestion doesn't help

[-] funkless_eck@sh.itjust.works 2 points 6 months ago

I know from running that 5k is 3.1miles so I just go from there

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[-] UnderpantsWeevil@lemmy.world 1 points 6 months ago

Which makes more sense than imperial units.

But you'd only need to do the conversion if you started with imperial units.

[-] Gloomy@mander.xyz 4 points 6 months ago

But woudn't you only need the 3 = 5 part?

[-] RememberTheApollo_@lemmy.world 8 points 6 months ago

Interesting, but if I have to look up a conversion I’ll just look up the actual conversion rather than an approximation.

[-] Hufschmid@sopuli.xyz 8 points 6 months ago

Why have brain when have computer

[-] pyre@lemmy.world 2 points 6 months ago

thanks to "AI" being in everything more and more computers are starting to perform worse than brain

[-] CompassRed@discuss.tchncs.de 4 points 6 months ago

The point is you don't have to look it up. Fibonacci is really easy to compute in your head.

[-] Huschke@lemmy.world 7 points 6 months ago

I always used "a little more than half".

[-] Tollana1234567@lemmy.today 6 points 6 months ago

isnt it easier to give them simple conversions 1mi=0.6km.

[-] SacralPlexus@lemmy.world 8 points 6 months ago

Might want to check your units.

[-] gwl 3 points 6 months ago* (last edited 6 months ago)

It's rough estimation, a deviation of anything less than 50% is accurate enough for that

Edit: Ooh I thought you were trying to "um actually, it's 1.66", but I just realised they put 0.6 instead of 1.6

[-] pupbiru@aussie.zone 5 points 6 months ago* (last edited 6 months ago)

or for in your head maths: half + 10%

(though it’s 1km=0.6mi, 1mi=1.6km)

[-] Sir_Premiumhengst@lemmy.world 6 points 6 months ago

Works because ratio of km to miles is about the golden ratio.

[-] SkunkWorkz@lemmy.world 5 points 6 months ago

I’m never going to visit the US or UK anyway.

[-] Routhinator@startrek.website 2 points 6 months ago

US and Israel are the only places that still use Imperial. While older generations in Canada and UK will speak about weight in Imperial, the official unit system is Metric.

[-] SkunkWorkz@lemmy.world 2 points 6 months ago

The UK still uses miles for vehicle speed and road signs

[-] Routhinator@startrek.website 1 points 6 months ago

That's strange. I would have thought with proximity to the EU the UK would have all metric signs like Canada.

[-] UnderpantsWeevil@lemmy.world 1 points 6 months ago

US and Israel are the only places that still use Imperial.

But the US has a global business empire. So you'll see the Imperial/Metric conversions all over the planet.

[-] RickyRigatoni@retrolemmy.com 5 points 6 months ago
[-] Kraven_the_Hunter@lemmy.dbzer0.com 3 points 6 months ago

That's the spirit.

Give it the ol college "why?"

[-] melsaskca@lemmy.ca 3 points 6 months ago

Cool! I wish I would have known this in the 70's when Canada changed over from British Imperial units to the Metric system. Maybe this is the incentive needed to push the usa into the rest of the metric system world!

[-] Mycatiskai@lemmy.ca 9 points 6 months ago

If every measurement being a factor of ten of a smaller or bigger unit isn't going to convince Americans of the ease of metric then the Fibonacci sequence isn't going to convince them.

[-] 33550336@lemmy.world 1 points 6 months ago

my upvote made 420 upvotes, coincidence?

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this post was submitted on 09 Nov 2025
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