[HN Gopher] Using Fibonacci numbers to convert from miles to kil...
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Using Fibonacci numbers to convert from miles to kilometers and
vice versa
Author : thunderbong
Score : 140 points
Date : 2024-08-28 13:48 UTC (2 days ago)
(HTM) web link (catonmat.net)
(TXT) w3m dump (catonmat.net)
| noman-land wrote:
| This is amazing.
| drivingmenuts wrote:
| Well, there's my new bar trick.
| _hao wrote:
| Pretty neat!
| OutOfHere wrote:
| The article shows:
|
| fn(n miles to km) [?] next_fib(n)
|
| fn(n km to miles) [?] prev_fib(n)
|
| ---
|
| Similarly,
|
| fn(n kg to lbs) [?] prev_fib(n) + next_fib(n)
|
| fn(n lbs to kg) [?] (prev_fib(n) - prev_fib(prev_fib(n))) * 2
|
| fn(fib(i) lbs to kg) [?] fib(i-1) - fib(i-4) # Alternate formula
| madcaptenor wrote:
| This is basically multiplying by sqrt(5) ~ 2.236, and 1 kg =
| 2.204 lb. Not bad!
| seanhunter wrote:
| Fun Fibonacci facts:
|
| - the first published use of the term "golden section" (which
| later became more commonly known as the "golden ratio") to
| describe the number phi[1] was by Martin Ohm, the brother of
| Georg Ohm who the unit is named after.
|
| - Binet's closed form series solution for the Fibonacci
| numbers[2] is really cool because it involves three irrational
| numbers yet every term of the resulting series is of course an
| integer.
|
| [1] (1+sqrt(5))/2
|
| [2] F(n)=(phi^n - psi^n)/ sqrt(5) (n=0,1,2,...) where
| phi=(1+sqrt(5))/2 and psi=(1-sqrt(5))/2
| LegionMammal978 wrote:
| Those are some amazingly spammy "Top Posts" at the bottom of the
| page. From the same blog, I thought at first that the "left-pad
| as a service" [0] was a parody, but the whole collection of
| Online Tools websites is so elaborate that it might truly be in
| earnest.
|
| Also, this should be (2010). The "last updated 3 weeks ago" is
| likely not real at all, every page on this blog was allegedly
| updated in a similar timeframe. (Maybe it counts every change to
| the list of links? Or maybe it's just bogus SEO nonsense.)
|
| [0] https://catonmat.net/1000-paying-left-pad-users
| hluska wrote:
| Why be a hater? It doesn't make you look smart. It just bores
| the rest of us.
| LegionMammal978 wrote:
| Because they've allegedly gotten hundreds to thousands of
| people to pay up to $9 per month for basic string utilities
| as a subscription service, just about all of which are
| offered for free by a dozen other websites. Either they're
| padding out their subscriber count by a lot, they have some
| impressive functionality they aren't advertising, or these
| subscribers are getting ripped off. Also, comparing to
| archived versions of the pricing page, they've been
| ratcheting up the price over time.
|
| Meanwhile, they're making some dubious claims about the
| security and privacy of their cloud browser service. Sure,
| _your_ ISP might not see which websites you 're visiting on
| it, but now _they_ can go snoop on your browsing however they
| 'd like, and read off all your passwords and whatnot.
| gjm11 wrote:
| I don't see any hate. I do see useful information. Looking at
| the linked page for myself, and seeing a list of "Top posts"
| all of which are obviously ad-infested SEO gunge, I
| immediately learn that I cannot trust whoever made the page,
| because getting eyeballs onto their advertisements is more
| important to them than truth.
|
| This doesn't have any particular implications for this
| particular page, and the "lucky 10,000" who had never before
| encountered the idea of converting between miles and
| kilometres using Fibonacci numbers will have learned
| something fun, which is great. But seeing the SEO bullshit
| tells me immediately that I am not going to want to (e.g.)
| add this blog to my feed aggregator[1].
|
| [1] Does anyone else actually use these any more? I feel a
| bit of a dinosaur.
|
| The grandparent of this comment was useful to me. Your "why
| be a hater?" was not.
| akira2501 wrote:
| > It just bores the rest of us.
|
| Yet you take the time to reply. This always baffles me.
| bawolff wrote:
| Surely its a parody. Like people can put lots of effort into a
| parody.
|
| Regardless, even if it wasn't, its at worst silly. Its not like
| he is scamming people out of money.
|
| Edit: after looking at a few more pages, now im not sure what
| to think. Maybe im wrong. The untracked browser stuff seems
| like it could be an actual scam on those who dont know what
| they are doing. Its all so much more extreme than i thought.
|
| Maybe this all is an attempt to link farm in order to get SEO
| to scam people. In which case it makes me feel complicit.
| a57721 wrote:
| I thought that the page about a service for padding strings was
| some kind of satire ("I promise I won't put it on npm, won't
| unpublish it, and I definitely won't rewrite it in Rust"), but
| apparently the website tries to sell such services, and overall
| it's a dumpster full of SEO spam and amateur JS coding
| exercises. Not a great link to see on HN.
| bena wrote:
| There's a slightly quicker way that they kind of stumble upon,
| but never outright say. miles * 8/5 = km and km * 5/8 = miles.
|
| How many km in 100 miles? 100/5 = 20, 20 * 8 = 160.
|
| How many miles in 400km? 400/8 = 50, 50 * 5 = 250.
|
| And 8/5 is 1.6 exactly, which is close to the "golden ratio".
| j0057 wrote:
| When driving in the UK, I found myself practicing my 16-table a
| lot: when seeing a 50 mph max speed sign, I'd multiply 5 by 16
| to get 80 km/h.
| gjm11 wrote:
| If you want _real_ accuracy, note that the actual mile /km
| ratio is almost exactly half way between 1.6 and (1+sqrt(5))/2.
| So do both conversions and take the average.
|
| (You won't get results as accurate as that suggests, of course,
| because doing the Zeckendorff + Fibonacci-shift thing only
| gives you an approximation to multiplying by (1+sqrt(5))/2.)
| tcdent wrote:
| > A pure coincidence that the Golden ratio is almost the same as
| kilometers in a mile.
|
| Is it really just a coincidence? Genuinely curious.
| plorkyeran wrote:
| Yes, of course.
| delecti wrote:
| Considering pre-metric France didn't use the mile, and the
| meter was originally meant to be 1/10,000,000 of the distance
| from the north pole to the equator, it seems almost impossible
| that it's intentional.
| ikawe wrote:
| The current "mile", the "International Mile", is very close to
| the 1593 "statute mile", going through a lot of history, but
| ultimately coming from 1,000 (a "mil") paces.
|
| The kilometer: As part of the widespread rationalization that
| occurred during the French revolution, the meter was defined in
| 1791 as 1 ten millionth the distance of a line drawn from the
| equator to the north pole, through Paris.
|
| Golden ratio: 1.618... km / mile ratio: 1.609...
|
| So, seems like just a coincidence.
|
| But these are fun:
|
| https://en.wikipedia.org/wiki/Mile
| https://en.wikipedia.org/wiki/Kilometre
| akira2501 wrote:
| > as 1 ten millionth the distance of a line drawn from the
| equator to the north pole, through Paris.
|
| Rationalized but nearly unrealizable.
| renewiltord wrote:
| Yes, of course. There are lots of these. pi ~= sqrt(g). Common
| trick to make period of pendulum approx = 2*sqrt(l) which is
| easy to calculate.
| madcaptenor wrote:
| But this one isn't a coinicidence - the idea of having the
| unit of length be the length of a seconds pendulum predates
| the meter we have. (It doesn't work because the period of a
| pendulum depends on your latitude.)
| renewiltord wrote:
| You're kidding me! That's a fact I had no idea about. I
| thought I was damned clever for having figured out the
| thing as a child and then found out all the other kids knew
| it too. I never thought to check the origin. Made my day.
| Thank you.
| umanwizard wrote:
| There was an HN post about the pi^2=g connection not too
| long ago.
| crdrost wrote:
| So it is, but the way that these units connect together is much
| closer than you'd think and amounts to a sort of mass
| distribution on the leg.
|
| The _kilometer_ is a thousand meters of course. And a _meter_
| was defined the way it was to match the length of a pendulum
| with a period of 2 seconds.
|
| The _mile_ was defined the way it was to match a different
| thousand: _a thousand Roman paces, measured as two steps_.
| (They didn 't like the fact that if you go from left foot to
| right foot the measurement is slightly diagonal, so they
| measured from left foot to left foot.) So if you figure that a
| Roman had a leg length, measured from the ball of the hip joint
| to the heel, say, as 80cm, and you figure that they marched
| like equilateral triangles, then the full pace is about 160 cm
| or 1.6 m, and the Roman mile is then ~1.6 km.
|
| But, my point is, these two numbers are not totally
| disconnected like it seems at first. So the second is a precise
| fraction of a day which has no direct connection to a person's
| leg. But, the decision to use this precise fraction is in part
| because when someone was looking at the 12 hours on the clock
| and placed the minutes and seconds, 5 subdivisions of the 24th
| part of the day looked and "sounded right." It is somewhat
| likely that this in part sounded right due to the standard
| Roman marching cadence, which was 120bpm (between footsteps) or
| 60bpm (left-foot-to-left-foot), set by your drummer, chosen
| presumably to maximize average efficiency among the whole unit.
|
| So then if we treat everyone's legs as a pendulum that is being
| driven slightly off-resonance, then the period of this leg
| motion is ~1 second and the leg behaves like a pendulum that is
| ~25cm long. And this kind of tracks! Measuring from the hip
| socket down 25cm gets near most folks' knees, the thigh is
| heavier than the calf so one would expect the center of mass to
| be up a little from the kneecap.
|
| So then you get that the leg is 80cm long from hip-socket to
| tip, but 25cm long from hip-socket to center-of-mass, and so
| you get some pure geometric ratio 2.2:1 that describes the mass
| distribution in the human leg, and that mass distribution
| indirectly sets the 1.6 conversion factor between km and miles.
|
| If we could only connect the human leg's evolutionary design to
| the Golden Ratio! Alas, this very last part fails. The golden
| ratio can appear in nature with things need to be laid out on a
| spiral but look maximally spread out given that constraint (the
| famous example is sunflower seeds), but all of the Vitruvian
| Man and "the golden ratio appears in the Acropolis" and
| whatever else aesthetics is kind of complete bunk, and there
| doesn't seem to be any reason for the universe to use the
| golden ratio to distribute the mass of the muscles of a leg. So
| you get like 98% of the way there only to fail at the very last
| 2% step.
| bloopernova wrote:
| If you find this neat, look into all the different calculations
| you can do on a Slide Rule:
|
| PDF link: https://www.sliderulemuseum.com/SR_Class/OS-
| ISRM_SlideRuleSe...
| sorokod wrote:
| "just express the original number as a sum of Fibonacci numbers"
|
| This is aways possible, see Zeckendorf's theorem.
|
| https://en.m.wikipedia.org/wiki/Zeckendorf%27s_theorem
| actinium226 wrote:
| As amusing as this is, I could not tell you offhand how to
| express 121 as a sum of fibonacci numbers. I mean I could
| figure it out, but I could also either multiply by 1.5 (121mi
| ~180km) or by 2/3 (121km ~80mi) and it would probably be a
| little bit faster than the fibonacci way.
| sorokod wrote:
| As suggested elsewhere, this is more of a party trick then a
| practical approach to convert between km and miles.
|
| The Wikipedia entry does suggest a greedy algorithm (at each
| step choosing the largest fib number that fits) though, using
| that we have
|
| 121 = 89 + 21 + 8 + 3
| yegle wrote:
| Call me snarky but instead of just multiply/devide by 1.6, you
| rather prefer remembering the Fibonacci numbers up to, I don't
| know, 200 to be useful?
| nrr wrote:
| In practice, at least in my experience, only up to 13. (Though,
| I have the sequence memorized up to 21 because of a sign
| outside Chattanooga[0], which is what gave me my "hey, wait"
| moment about this.)
|
| A combination of both the fundamental theorem of algebra and
| Zeckendorf's theorem has allowed me to fill in the rest so far.
| For example, 25 mi = 5 * 5 mi, which yields 5 * 8 km = 40 km.
| As it turns out, that is how far Cleveland, TN, lies from
| Chattanooga.
|
| 0: https://usma.org/metric-signs/tennessee
| battles wrote:
| That's what I was thinking. I good example of over-engineering
| though.
| jmholla wrote:
| Yea, and since it's the golden ratio, the division is roughly
| the same as multiply by 60%. So you can just remember to take
| 60% and add it to the original or treat it as the answer
| depending on if you're going to or from the smaller
| measurement.
| btilly wrote:
| The list isn't that long. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
| and 144.
|
| I memorized this almost by accident. I was doing hand rolled
| spaced repetition system for conditioning myself to fix some
| bad habits, and they came up often enough that it was
| memorized.
| jraph wrote:
| It's art. It's possibly not very useful (who knows, though?),
| but some will find beauty, joy, entertainment, surprise,
| amazement, incredulity, anger, disdain, indignation, fear,
| nostalgia in this. Others will feel the deepest and purest
| indifference.
| starktyping wrote:
| this has Rube Goldberg energy if you have seen the Golden Ratio
| connection or derived Binet's formula before - my first thought
| was "yeah because the conversion and the golden ratio are both
| 1.6ish"
| pg_bot wrote:
| A mile is 5,280 feet and a kilometer is approximately 3,280 feet.
|
| If you need to do rough conversions just think of a kilometer as
| slightly more than 3/5ths of a mile.
| namrog84 wrote:
| If remembering a fraction or number. I always felt like it was
| easier to remember 100kph is 62mph or basically close to a mile
| a minute.
| riccardomc wrote:
| > just think of a kilometer as slightly more than 3/5ths of a
| mile.
|
| I can confidently assure you that right about now there are a
| bunch of Europeans reading your message multiple times, trying
| to figure out what 3/5ths of a mile even means, asking
| themselves if this is satire.
| thechao wrote:
| It's the same ratio as 28 3/4 tsp to a cup.
| theendisney wrote:
| You are doing it wrong.
|
| A kilo meter is 1000 meter like a kilo gram is 1000 gram.
|
| A land mile is 1609.344 meter.
|
| 16 is easy to remember as a symbol of immaturity but you do get
| to drive in the us. Not in the eu _nein_
| dwe3k wrote:
| I find it interesting, but I question how practical it is for
| regular use.
|
| On a recent trip, I was driving in Canada in a car bought in the
| United States that did not have the metric values on the
| speedometer. But all of the posted speed limits were in values of
| 5 kph. Once you get that (roughly) 100 kph = 62 mph and 10 kph =
| 6 mph, there are some simple quick divisions or subtractions to
| convert the speed limit to close enough.
|
| - 50 kph = (100 kph) / 2 = 62 mph / 2 = 31 mph
|
| - 80 kph = 100 kph - 2 * 10 kph = 62 mph - 2 * 6 mph = 50 mph
| Taek wrote:
| I use the fib conversions quite regularly.
|
| Both of your examples are actually easy Fibonacci numbers.
|
| 50kph - 5 is a fib number, and the previous number is 3. I can
| go 50->30 without any math at all.
|
| And 80kph, well 8 is also a fib number. And the previous is 5.
| I can go 80->50 without any math at all.
|
| 120kph is close to 13, so I know 120kph is somewhere below
| 80mph. I always divide any remainder by 2, so I would quick
| math my way to 120->75. That's accepatably close to the real
| answer of 74.4
|
| Same thing with 110kph. That's close to 13, so I'd quick math
| to 70 mph (130->80, remainder is 20, subtract half the
| remainder). That's acceptably close to the real answer of 68.2
| function_seven wrote:
| I always just use either 6/10 or 2/3, depending on which one is
| easiest to do in my head.
|
| Yes, this means both 90 and 100 km/h both covert to 60mph.
| Close enough!
| mikewarot wrote:
| Tangentially - If it weren't for the arbitrary decision of Carl
| Johansson, converting lathes from metric to imperial units
| wouldn't be exact. Thanks to him, an inch == 2.54 cm exactly.[1]
|
| This means you can use a 50 and 127 tooth gear pair to do
| conversions and make metric threads accurately on an imperial
| lathe, and vice versa.
|
| [1]
| https://en.wikipedia.org/wiki/Carl_Edvard_Johansson#Johansso...
| cryptonector wrote:
| I do this all the time.
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