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

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.

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

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

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

How often you drive 200mph??

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.

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.

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

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.

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

Yes, of course.

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.

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.

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.

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

> 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

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.

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

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.

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.

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

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

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!

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

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.

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.

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.

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.

> 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.

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.

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.)

Don’t all cars have both units?

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.

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.

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.

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.

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