[HN Gopher] Using Fibonacci numbers to convert from miles to kil...
___________________________________________________________________
Using Fibonacci numbers to convert from miles to kilometers and
vice versa
Author : thunderbong
Score : 339 points
Date : 2024-08-28 13:48 UTC (3 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.
| hluska 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.
|
| If you don't see the hate in statements like that, I
| question your empathy. What would be wrong with talking
| about the actual content in the article?
|
| For all you know, the author downloaded a theme and doesn't
| care in the slightest. But you don't have enough empathy to
| consider that so you'll close your mind to what could
| potentially help you think differently.
|
| Hate over stupid things is remarkably boring. Deal with
| facts - they're helpful.
| gjm11 wrote:
| I do, in fact, know that the author didn't "download a
| theme", because all those spammy "Top Posts" link to
| things advertising _the author 's products_.
|
| I am curious as to whether you truly think that
|
| > Those are some amazingly spammy "Top Posts" at the
| bottom of the page.
|
| shows more hate and less empathy than
|
| > But you don't have enough empathy to consider that so
| you'll close your mind to what could potentially help you
| think differently.
|
| It seems the other way around to me, though of course my
| opinion will be biased by the fact that one of them is
| being negative about _me_ and the other about _the maker
| of some random blog on the interwebs_. (Though ... I tend
| to think that any given negative remark shows more hate
| and less empathy when it 's made directly to the person
| it's about. Compare "X isn't terribly bright" with "You
| aren't terribly bright".)
| akira2501 wrote:
| > It just bores the rest of us.
|
| Yet you take the time to reply. This always baffles me.
| hluska wrote:
| If that truly baffled you, you wouldn't have replied to me.
| akira2501 wrote:
| The purpose of conversation is to reveal facts previously
| unknown. If I'm baffled by it, you should absolutely
| expect me to reply.
|
| If I told you you were being boring, you should wonder
| why I would bother to reply, or if I'm being dishonest in
| an effort to be hurtful.
| 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.
| robertlagrant wrote:
| Hah I've just been driving in France and kept multiplying by
| 0.6. Much simpler than 16!
| 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.
| ahazred8ta wrote:
| The distance from pole to equator is 90*60 = 5400 nautical
| miles, and the same distance is 10,000 km. So for a long time
| the km was exactly 0.54 nautical miles.
| 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.
| madcaptenor wrote:
| It's come up several times.
| 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...
| litoE wrote:
| My Breitling watch has a built-in circular slide rule. When in
| a foreign country, I set it (once) to the local currency
| exchange rate, and can quickly convert how much anything costs
| into dollars. I could do the same with the calculator on my
| phone, but I would have to key in the exchange rate every time
| - if I can even remember what it is.
| tgv wrote:
| I've got a circular slide rule (not really a rule, is it?)
| with square and cube values, so you can convert surface and
| volume. Conversion numbers are printed on the back. It seems
| to have been made as a cheap handout. Not that I ever use it,
| but it's a cool idea.
| 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
| pavon wrote:
| I do think that it has practical applications for the
| smaller ratios that are easy to remember and/or derive. For
| example 5:8 is a both a closer approximation than 3:5 that
| most people use, and is more convenient when miles are a
| multiple of 5.
| outop wrote:
| One problem with this is that it decomposes 2 * 55 to 89 +
| 21, etc which makes the conversion slightly harder than
| just converting 55 and doubling.
| outop wrote:
| Also the decomposition of 88 is 55 + 21 + 8 + 3 + 1. A
| lot of terms just to find that phi * (Fn - 1) is (F{n+1}
| - 1) which isn't even very accurate.
| pedrovhb wrote:
| Or by the definition that the ratio between consecutive fib
| numbers approaches Phi, just multiply by 1.618? Though at
| that point might as well just use the real conversion ratio.
|
| In other news, p2 [?] g.
| DylanDmitri wrote:
| For 121, I ratio 130:80, then because I started ten under I
| subtract half that at the end. So about 75.
| eapriv wrote:
| This is always possible, because 1 is a Fibonacci number.
| sorokod wrote:
| That is true, the article skips the fact that the
| approximation using the initial fib numbers is not useful.
| gilleain wrote:
| from the wiki page:
|
| "Zeckendorf's theorem states that every positive integer can
| be represented uniquely as the sum of one or more distinct
| Fibonacci numbers in such a way that the sum does not include
| any two consecutive Fibonacci numbers."
|
| so, distinct and non-consecutive
| eapriv wrote:
| Sure, but the conversion method does not require the
| numbers to be distinct or non-consecutive.
| muti wrote:
| Non consecutive isn't surprising, any consecutive Fibonacci
| numbers in the sum can be replaced with their sum, which is
| itself a Fibonacci number by definition
| lupire wrote:
| That's not sufficient to be unsurprising.
|
| What if a sum has more than 2 consecutive Fibonacci
| numbers? That doesn't cause a problem, but it takes a
| little more work to sort it out.
| 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
| sigmoid10 wrote:
| >A combination of both the fundamental theorem of algebra and
| Zeckendorf's theorem
|
| How do you apply the fundamental theorem of algebra here?
| battles wrote:
| That's what I was thinking. I good example of over-engineering
| though.
| dylan604 wrote:
| Some people think differently. Some methods click with some
| people, while making others think it's making it overly
| complicated. The new math drove people crazy. The concept of
| doing extra math by rounding a number up to a whole number,
| and then subtracting the diff seems like a lot of work, but
| is amazing when used frequently to do "in your head" type of
| work. That extra match can lead to an answer faster than
| traditional math
| 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.
| jameshart wrote:
| Just spend a few sprints in a sufficiently dysfunctional
| agile team and you'll learn all sorts of higher Fibonacci
| numbers.
| Terr_ wrote:
| Technically they could also also be functional teams with a
| long history of gradual point drift... Though most
| organizations shake teams up before then.
| btilly wrote:
| If a ding that gets mentioned in planning is 1 point and
| they regularly try to fit 144 point projects in a sprint
| without splitting it up, that's likely to be rather
| dysfunctional.
|
| I mean it is possible that gradual point drift would get
| there. But sufficiently improbable that I know what I'm
| betting on.
| shultays wrote:
| For some reason we are using 20 instead of 21. I didn't
| even bother asking why
| rahkiin wrote:
| That is because fibonacci is used to indicate the
| 'guess'timation part. 5 Instead of 'twice as much work as
| a 2' (4). The idea is when you get higher numbers the
| opposite happens: 21 sounds like a very specific number
| and not like a rough guess. 20 does.
|
| So it becomes 1 2 3 5 8 13 20 40 inf ?
| dgfitz wrote:
| By that logic shouldn't people just do 1 2 3 5 10 15 20?
| outop wrote:
| Yes, but remembering the multiples of 10 is vastly easier:
| they are 10, 20, 30, 40, etc. Remembering the multiples of 16
| is quite a lot easier: 16, 32, 48, 64 etc. You probably
| already know them.
|
| Now to convert from miles to km replace a multiple of 10 by a
| multiple of 16. 70 mph becomes 112 km/h.
|
| To convert in the opposite direction do the opposite. 130km/h
| is 128 km/h + 2 km/h = 80mph + 1 mph (rounding down since you
| don't want to have to justify this calculation at the side of
| the road, to a gendarme, in a foreign language).
|
| 1.6 km = 1 mile is just as accurate as using 1.618.., the
| golden ratio. (Enough for driving, not enough for space
| travel.) And using the Fibonacci method is less accurate than
| the golden ratio since small Fibonacci numbers are only
| approximately the golden ratio apart.
|
| The only possible justifications for the Fibonacci method
| are:
|
| 1. You want people to know that you know what the Fibonacci
| sequence is.
|
| 2. You enjoy overengineering.
|
| 3. You're one of quite a few people who believe, for whatever
| reason, that the golden ratio appears all over the place like
| in measurements of people's belly buttons, the Great
| Pyramids, and so on, and that this has some spiritual or
| mathematical significance.
| 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.
| JustSomeNobody wrote:
| How often you drive 200mph??
| yegle wrote:
| I think it's more common to convert distances.
|
| I consider any distance reachable with one tank of gas
| commonly used (so up to 400 miles).
| amarcheschi wrote:
| I'm even lazier, 1.6 might be hard to do without a Calc, I just
| grab 50% of the original number, 10%, and then sum them to the
| original
| throwadobe wrote:
| That's how I do many kinds of percentages... like 72% is 50%
| and then 10% twice and then a couple of 1%s
| huhtenberg wrote:
| In the same vein, converting pounds to kilos is "divide by 2,
| subtract 10%".
| amarcheschi wrote:
| no way just discovered this lmao i now only need a similar
| thing for fahrenheit to c/viceversa, i'm sure it exists.
| however, i'm so lazy i will not search for that information
| now
| venusenvy47 wrote:
| For Celsius to Fahrenheit, just double it and add 30. It
| gets you pretty close for the temperature range that
| humans live in.
| comradesmith wrote:
| Here's a practical solution based on this:
|
| Take your kilometres e.g 60, divide by 5 -> 12, now times that
| by 3 -> 36.
|
| Take your miles e.g 80, divide by 5 -> 16, times 8 -> 80 + 48
| -> 128
|
| So any conversion reasonable conversion can be done in your
| head with your 3, 5, and 8 times tables
| 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.
| pg_bot wrote:
| It's approximately one kilometer.
| 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_
| jameshart wrote:
| Sure you can use 3/5 - an easy Fibonacci fraction. Or about
| 5/8. Or 8/13. These fractions have the advantage of being easy
| to produce and having different prime factors that cancel more
| easily with some numbers.
| ordu wrote:
| _> A mile is 5,280 feet and a kilometer is approximately 3,280
| feet._
|
| Wow, I didn't think of poor imperial kids, that are definitely
| forced to remember all these numbers. But now I'm really sorry
| for them. $ factor 5280 5280: 2 2 2 2
| 2 3 5 11
|
| 2^5 and 5 is nice, 3 can be tolerated, but 11? Who in their
| right mind would come up with something like this? Why not just
| round it to 5000?
| QuercusMax wrote:
| In practice these are just big numbers you memorize. 5280
| feet in a mile, 63360 inches in a mile, 1760 yards in a
| mile...
|
| It's not like you often have to do math with them, outside of
| school math problems. A year isn't precisely 365 days, and
| months are all different lengths. It's just more of the same
| type of thing; doesn't actually cause problems when distances
| are usually expressed in miles anyway.
| remram wrote:
| From polling my American friends, ask them how many yards
| in a mile and they'll answer 5280. They don't really know
| how the system work and can only vaguely remember (one of)
| these numbers.
|
| The system is not meant for units to be converted.
| ahazred8ta wrote:
| Up until 1300, the old foot was longer and the mile was 5000
| feet. In 1300 they redefined 10 old feet to be 11 new smaller
| feet, an acre was now 66x660 feet instead of 60x600, and
| eventually the mile was 8x660 = 5280.
| Taniwha wrote:
| having lived thru switching from miles->km you learn a few
| simple rules of thumb:
|
| 100km==60miles 80==50 50==30
|
| It helped that that also covered most of our posted speed
| limits - the US with its penchant for speed limits ending in 5
| would find it harder going
| 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
| jameshart wrote:
| Instead of halving the remainder, you can do 3/5 - since it's
| always going to be a multiple of five - so 120kph is going to
| be more like 74mph because it's 10kph less than 130, and
| 10kph=2 _5kph[?]2_ 3mph=6mph
|
| Also, this doesn't only work with Fibonacci numbers, it works
| with any Lucas sequence, since they all tend to phi, so as
| well as 2-3-5-8-13 you can also use the higher numbers from
| 1-3-4-7-11 to fill in some gaps and help estimate.
|
| And as a bonus, it means if you know A kph is equal to B mph,
| you also know that A mph is ~equal to A+B kph.
|
| So given your result above of 120kph=74.4mph, I would
| estimate 120mph[?]194kph. And it turns out it's actually
| 193.1koh, so... not far off.
| chillingeffect wrote:
| To mult by 1.6: double it four times then divide by 10. Eg.
| 55mph = 110, 220, 440, 880, 88.0 kph
|
| To divde by 1.6, multiply by 10, then divide by 2 4x. Eg :
| 200 kph, 2000, 1000, 500, 250, 125 mph
| pacaro wrote:
| I guess that I was taught basic mental arithmetic
| differently. Multiply by 8 and divide by 5, or (it's
| inverse) is two single instruction cycle opcodes (or
| whatever my brains equivalent is).
|
| Regularly needing to translate between sane units and US
| (and occasional British) idiosyncrasies keeps these
| mental muscles worked enough that it's mostly
| subconscious now.
|
| I didn't enjoy rote repetition of times tables and drills
| as a kid, but it's frustrating seeing my daughter being
| taught to understand multiplication, and learning
| "strategies", but struggling with mental arithmetic (I
| mean she tests above grade level, so I'm not worried,
| it's just a _get off my lawn_ reflex)
| jameshart wrote:
| Arithmetic strategies are great but you still need a
| bunch of quick operations (like doubling and multiplying
| by 10) and fundamental lookup tables (like basic
| multiplication tables, squares, powers of two) to
| bootstrap them from.
|
| I don't think knowing all the times tables up to 12 is as
| helpful as having a good appreciation for how to break a
| multiplication into simpler parts, but you do need
| immediate recall on multiples of all the single digit
| numbers, up to at least times five or six.
| 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!
| I_complete_me wrote:
| 6/10 = 5/10 + 1/10 or in words: divide by two and add a
| tenth!
| dgfitz wrote:
| Is it because of how you do mental math? I saw 6/10 and
| immediately mentally registered 3/5, which is a simpler
| number to mental math with, for me anyways.
| 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...
| samatman wrote:
| Every time this is mentioned I feel a wild flash of anger that
| he didn't set it to 2.56cm.
|
| That would make the inch precisely (1/10 000)^8 meters.
|
| Instead, we're stuck with almost that. Forever.
| cryptonector wrote:
| I do this all the time.
| kylehotchkiss wrote:
| KM to MI shortcut: divide by 2 and add 7. Not super accurate but
| makes driving through Canada a little easier.
| epgui wrote:
| Don't all cars have both units?
| dylan604 wrote:
| For speed, yeah, but for distance? Still need to convert in
| the head while driving.
| dktalks wrote:
| This is a good theory but the basic maths is that 1 mile = 1 km *
| 1.6 or vice versa. This is the basic thing you need to do.
|
| However, this can get confusing it it get's to odd numbers etc,
| so what you can do is, simple leave it as miles because if you
| are in a miles country no one is converting it to km or vice
| versa.
|
| Same with C and F in temperatures, there are basic maths systems
| that can do this in constant time, so there is no real reason to
| complicate it unless you want to do it in your head and then
| there is the basic maths to do it, if you can't just use a
| calculator.
| orourkek wrote:
| > if you are in a miles country no one is converting it to km
| or vice versa
|
| My relatives & friends visiting from Europe often appreciate
| knowing such values in km/C. There are various other reasons to
| want to do the conversions too, and sometimes speed > accuracy.
| It's a bit ridiculous to think that _no one_ is doing these
| conversions and that shortcuts/approximations like this are not
| useful.
| ziddoap wrote:
| > _simple leave it as miles because if you are in a miles
| country no one is converting it to km or vice versa._
|
| Maybe true in a miles country, I'm not sure.
|
| However, so much stuff posted on the internet just assumes you
| are from the states, so they use imperial measurements only,
| and most of the rest of the world _does_ need to do these
| conversions. I 'm converting on an almost daily basis.
| Symbiote wrote:
| It's a minor peeve of mine that many people assume English
| means miles and pounds, when there are millions of tourists
| etc reading the English signs who want the original, metric
| measurements.
| dhosek wrote:
| Is this really easier for people than simply multiplying by 5/8
| or 8/5 as appropriate? And how often does one need to do this
| conversion anyway? I definitely don't have any fibonacci numbers
| above 13 memorized.
| ordu wrote:
| _> Is this really easier for people than simply multiplying by
| 5/8 or 8/5 as appropriate?_
|
| I usually just treat miles as kilometers. When I need more
| precision I multiply miles by 1.5. All these 8/5 just don't
| stick in my mind, and 1.6 is not much better then 1.6, but it
| is much easier to multiply by 1.5.
|
| _> And how often does one need to do this conversion anyway?_
|
| Every time I see distance measured in miles. It may be 1 time
| per week, or multiple times per day.
| jojobas wrote:
| >I usually just treat miles as kilometers.
|
| I'll take "things not to say to a cop" for 300 Alex.
| madcaptenor wrote:
| Alex isn't the host any more and there hasn't been a 300 in
| a very long time.
| habibur wrote:
| "how many kilometers are there in 100 miles?"
|
| Increase by 60%. That's how I do it.
| IAmGraydon wrote:
| Or you could...you know...multiply the number of miles by 1.609
| or divide the number of kilometers by the same to get the actual
| correct answer. The fact that miles/km is close to the golden
| ratio is what we call a coincidence, and I'm really unsure why
| anyone finds this to be interesting.
| luxuryballs wrote:
| How does he know it's a coincidence?
| henearkr wrote:
| Nice! The wow effect was enough to imprint it into my mind.
|
| Now I'm waiting for something that cool for Celsius and
| Fahrenheit...
| igornadj wrote:
| I use Everything Metric
| (https://chromewebstore.google.com/detail/everything-metric-a...)
| tzs wrote:
| One nice thing about mi/km conversions (and / conversions which
| have been mentioned in the comments) is that once you have a way
| to do them mentally that works well for you, you are done.
|
| I once worked out a way to quickly figure sales tax for my area
| using just a small number of operations that are easy to do in my
| head.
|
| "Easy" means that it just involved things like taking 10%, or
| multiplying or dividing by 2, or adding or subtracting, or
| rounding to a given precision, and that it did not require
| keeping too many intermediate results in memory.
|
| It worked great. And then the sales tax rate changed.
|
| I have a vague recollection of then writing a program that would
| brute force check all short combinations of my "easy" operations
| to find ones that worked for a given tax rate. But I can't find
| that program now, and may have only thought about writing it.
| maxerickson wrote:
| If you just need the rough estimate, round up and multiply is
| pretty universal.
|
| Doesn't work if you are trying to decide if you have enough
| change to buy something of course.
| mauvehaus wrote:
| For practical applications, multiplying by 16/10 or 10/16 is
| pretty easy and doesn't require memorizing or calculating
| Fibonacci numbers.
|
| In your head you can multiply or divide by two four times and
| move the decimal point once when it's most convenient or best
| facilitates further multiplication or division.
| stouset wrote:
| I just use 3/2 and 5/3. Both of them are "close enough", and
| one of the two is generally trivial to do in your head with
| numbers found in the wild.
| lupire wrote:
| That's a Fibonacci ratio. But smaller Fibonaccis are less work
| for less accuracy.
| scarmig wrote:
| Challenge: find other sequences that you can use to convert,
| using integer coefficients in the recurrence. For miles to
| kilometers, you have to get a better approximation than phi.
|
| I wasn't able to for miles to kilometers, but for pounds to
| kilograms I got:
|
| a_n = a_{n-1} + 4*a_{n-2} - 3*a_{n-3}
|
| Converges (slowly!) to a ratio of 2.199, so you can then take the
| previous term of the sequence to convert from pounds to
| kilograms.
| dirtdobber wrote:
| Interviewer: "Write a Th(log(n)) approximation algorithm for
| converting n miles to kilometers that's accurate within plus or
| minus .01*n kilometers."
| garrettgarcia wrote:
| def m2k(n): return n*1.609344
|
| There, did it in O(1)
| dirtdobber wrote:
| I said th ;)
|
| In other words, your algorithm is asymptotically too fast and
| you failed the interview! :D
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