Using Fibonacci numbers to convert from miles to kilometers and vice versa

https://catonmat.net/fibonacci-miles-kilometers

by thunderbong • 2 years ago

362 129 2 years ago

catonmat.net

noman-land• 2 years ago

This is amazing.

drivingmenuts• 2 years ago

Well, there’s my new bar trick.

_hao• 2 years ago

Pretty neat!

OutOfHere• 2 years ago

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

madcaptenor4• 2 years ago

This is basically multiplying by sqrt(5) ~ 2.236, and 1 kg = 2.204 lb. Not bad!

seanhunter• 2 years ago

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

LegionMammal9782• 2 years ago

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

hluska3• 2 years ago

Why be a hater? It doesn’t make you look smart. It just bores the rest of us.

LegionMammal9782• 2 years ago

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.

gjm113• 2 years ago

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.

akira25013• 2 years ago

It just bores the rest of us.

Yet you take the time to reply. This always baffles me.

bawolff• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

Hah I've just been driving in France and kept multiplying by 0.6. Much simpler than 16!

NikkiA• 2 years ago

Given (official*) UK speed limits are always in multiples of 5, using the 8/5 rule would be quicker and work just as well.

* There are occasional places where private property has speed limits with weird factors, but they're so rare as not to worry about. (the one example I remember is when I used to cycle to work and took shortcuts through a sewage plant that had an '11 mph' speed limit, why? who knows.

gjm113• 2 years ago

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• 2 years ago

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• 2 years ago

Yes, of course.

delecti• 2 years ago

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• 2 years ago

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

akira25013• 2 years ago

as 1 ten millionth the distance of a line drawn from the equator to the north pole, through Paris.

Rationalized but nearly unrealizable.

ahazred8ta2• 2 years ago

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.

renewiltord2• 2 years ago

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.

madcaptenor4• 2 years ago

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.)

crdrost• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

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.

sorokod3• 2 years ago

"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• 2 years ago

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.

sorokod3• 2 years ago

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

pedrovhb• 2 years ago

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, π² ≈ g.

DylanDmitri• 2 years ago

For 121, I ratio 130:80, then because I started ten under I subtract half that at the end. So about 75.

eapriv2• 2 years ago

This is always possible, because 1 is a Fibonacci number.

sorokod3• 2 years ago

That is true, the article skips the fact that the approximation using the initial fib numbers is not useful.

gilleain• 2 years ago

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

yegle2• 2 years ago

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• 2 years ago

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• 2 years ago

A combination of both the fundamental theorem of algebra and Zeckendorf's theorem

How do you apply the fundamental theorem of algebra here?

battles• 2 years ago

That's what I was thinking. I good example of over-engineering though.

dylan6042• 2 years ago

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• 2 years ago

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.

btilly2• 2 years ago

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.

jameshart4• 2 years ago

Just spend a few sprints in a sufficiently dysfunctional agile team and you’ll learn all sorts of higher Fibonacci numbers.

outop3• 2 years ago

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• 2 years ago

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• 2 years ago

How often you drive 200mph??

yegle2• 2 years ago

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).

amarcheschi2• 2 years ago

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• 2 years ago

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• 2 years ago

In the same vein, converting pounds to kilos is "divide by 2, subtract 10%".

comradesmith• 2 years ago

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• 2 years ago

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_bot2• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

It's the same ratio as 28 3/4 tsp to a cup.

pg_bot2• 2 years ago

It's approximately one kilometer.

theendisney• 2 years ago

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

jameshart4• 2 years ago

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.

ordu2• 2 years ago

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• 2 years ago

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.

ahazred8ta2• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

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

jameshart4• 2 years ago

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=25kph≈23mph=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.

function_seven2• 2 years ago

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• 2 years ago

6/10 = 5/10 + 1/10 or in words: divide by two and add a tenth!

dgfitz2• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

I do this all the time.

kylehotchkiss• 2 years ago

KM to MI shortcut: divide by 2 and add 7. Not super accurate but makes driving through Canada a little easier.

epgui• 2 years ago

Don’t all cars have both units?

dylan6042• 2 years ago

For speed, yeah, but for distance? Still need to convert in the head while driving.

dktalks• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

Is this really easier for people than simply multiplying by ⅝ 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.

ordu2• 2 years ago

Is this really easier for people than simply multiplying by ⅝ 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• 2 years ago

I usually just treat miles as kilometers.

I'll take "things not to say to a cop" for 300 Alex.

habibur• 2 years ago

"how many kilometers are there in 100 miles?"

Increase by 60%. That's how I do it.

IAmGraydon• 2 years ago

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• 2 years ago

How does he know it’s a coincidence?

henearkr• 2 years ago

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• 2 years ago

I use Everything Metric (https://chromewebstore.google.com/detail/everything-metric-a...)

tzs• 2 years ago

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• 2 years ago

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• 2 years ago

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• 2 years ago

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.

lupire2• 2 years ago

That's a Fibonacci ratio. But smaller Fibonaccis are less work for less accuracy.

scarmig• 2 years ago

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.

dirtdobber2• 2 years ago

Interviewer: "Write a Θ(log(n)) approximation algorithm for converting n miles to kilometers that's accurate within plus or minus .01*n kilometers."

garrettgarcia• 2 years ago

def m2k(n): return n*1.609344

There, did it in O(1)

dirtdobber2• 2 years ago

I said θ ;)

In other words, your algorithm is asymptotically too fast and you failed the interview! :D

cben2• 2 years ago

I learnt this from Concrete Mathematics (Graham, Knuth, Patashnik). Don't remember if main text or the side notes of accumulated student wisdom... (I dont mean on my copy, this textbook is _printed_ with tons of amusing/insightful side notes)

They also mention _approximate_ cm/inch conversion is doable by double shift on the Fibonacci scale - if golden ratio was exactly 1.6, its square would be 2.56, but actual phi² = 2.618 which is quite bad approximation for 2.54...

Using Fibonacci numbers to convert from miles to kilometers and vice versa

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