This is because fibonacci numbers approach golden ratio which is approximately 1,618033... and one mile is 1,609344 kilometres exactly.
Lifehacks
Efficiency in all walks of life.
You can use kilometres
Nah, that's too difficult for USAians. They can memorize fibonacci numbers much more easily.
Be like us Brits and measure short distances in metric, long distances in Imperial, yet struggle to convert between them.
GPS navigation gets frustrating. It's either metric "turn left in 4km" when all road signs and speeds are in miles, or imperial "turn in 200ft" when you have no idea how long 200ft is.
I never understood the use of yards for exits over there, but the hardest part was figuring out what my GP meant when he said I needed to lose a couple 'stones'... C'mon, you can't expect me to learn imperial, metric, and whatever the hell that is.
I'm already stuck having to be able to convert between elephants and F-250's because my homeland REFUSES the metric system, now I have to study geology just to figure out how unhealthy I am (actually was, I've lost 40lbs since then).
Hey I’m going to have to ask you to censor that word. There’s American children on this ap! We can’t have them going to the playground and repeating that kind of language.
H A T E S P E E C H
🚨🚨 A L E R T 🚨🚨
🦅🦅🦅
And yet the military uses "clicks"
Just gotta ask any of the 90% of the world who use it to find out. Americans hate this one simple trick!
Fun fact: there's quite a lot of countries that use "mixed metrics", with no real rhyme or reason for what uses old ancient imperial and what uses new shiny metric
UK - Miles for long distances, switch to meters for distances less than a mile, always use km in air and sea. Milk in pints, petrol in liters, water in ml, beer in pints. Human heights in Feet Inches, building heights in Meters. Human weights in a unit even Americans don't use anymore (Stone), animal weights in kg/g.
Really? Do people walk around in the UK and say "I weigh 11 stone"? "I lost 3 stone on this diet"?
Canadian here, I watch some UK fitness shows, can confirm.
Canada another that does the Mixed Metrics, but with entirely different sets of arbitrariness
Yessir, stone and lbs usually.
So 12 stone 8 for example. 14lbs to the stone.
Yeah, but does the kilometer have a cool origin like the mile? Checkmate math nerd.
I'd say it kind of does actually:
The Kilometer is defined as one ten-millionth of the distance from the Earth's North Pole to the equator along the meridian passing through Paris.
Vs
The mile originated with the Roman measurement of mille passus, meaning "one thousand paces," with a pace being five Roman feet. The modern 5,280-foot statute mile evolved in England, where the 1592 parliamentary act defined the mile as eight furlongs (660 feet each) to standardize the distance.
One is measured by earth, the other by stinky feet.
Yeah but earth is wobbly and imprecise so now we define the meter as "the distance light travels in a vacuum in 1/299,792,458th of a second"
That'a a cool definition. I wouldn't call it an origin though, that would still be the Earth measurement through Paris, which is also cool.
0.54 nmi (nautical miles)
Interesting, but if I have to look up a conversion I’ll just look up the actual conversion rather than an approximation.
Why have brain when have computer
thanks to "AI" being in everything more and more computers are starting to perform worse than brain
The point is you don't have to look it up. Fibonacci is really easy to compute in your head.
I always used "a little more than half".
This is such a cool example of how some recursive algorithms have a closed form. We all know that there's a simple equation to plug miles into to get kilometers, but we don't talk about how the Fibonacci sequence has a closed form. This is so cool.
Wjat does closed form mean? Asking as a stupid botanist, sorry.
Closed form means it can be written out as a specific, finite set of instructions that work the same regardless of what the input to your function is.
For Fibonacci, it is most commonly defined in its recursive form:
f(0) = 0
f(1) = 1
f(x) = f(x-1) + f(x-2) for integer x > 1
But using this form, computing a very large Fibonacci number requires computing all the numbers before it, so it’s not the same finite set of instructions for every number, it takes more computation to generate larger numbers.
However, there is a closed form formula for generating Fibonacci numbers. Using this formula, you can directly compute any large Fibonacci number without having to compute all those intermediate steps. It takes the same amount of work to compute any Fibonacci number.
f(x) = (a^x - b^x)/√5
a = (1+√5)/2
b = (1-√5)/2
(Note that a and b here are constants; I only wrote them separately to avoid a mess of nested parenthesis)
For an example of something that doesn’t have a closed form, we do not know of a closed form for generating prime numbers. There are several known algorithms for generating the nth prime number, but they all depend on computing all the previous prime numbers, making it very difficult to compute very large prime numbers (in fact, how generating large primes is actually done is by making an educated guess and then checking that it’s actually prime). Discovering a closed form formula for prime numbers would have a huge impact on mathematics and cryptography.
Thank you. So does that mean that the Fibonacci can help us because just like the miles-km algorithm it is closed form, so we can use it to compute a single number, and at the same time it gives us similarish results because of coincidence?
Works because ratio of km to miles is about the golden ratio.
To go from km to mi I always leaned “multiply by 6 and move the decimal one to the left”. So 6km is ~3.6mi. Or 10km is just about 6mi.
Yes. That uses the 3:5 ratio.
isnt it easier to give them simple conversions 1mi=0.6km.
Might want to check your units.
It's rough estimation, a deviation of anything less than 50% is accurate enough for that
Edit: Ooh I thought you were trying to "um actually, it's 1.66", but I just realised they put 0.6 instead of 1.6
or for in your head maths: half + 10%
(though it’s 1km=0.6mi, 1mi=1.6km)
Ah yes, I always remember the Fibonacci sequence and totally wouldn't find it harder to calculate than just doing the conversion the regular way
/sarcasm
But woudn't you only need the 3 = 5 part?
"Remember"? Do you also remember all the digits of π?
It's defined as F(0) = 0, F(1) = 1 and F(n) = F(n - 1) + F(n - 2). Which makes more sense than imperial units.
Or I could just do 1.6 km ≈ 1 mile whenever I need to convert from the standard that I use, Metric, to Imperial
Far far far simpler
Edit: I'm not American, I use sensible units, SI Metric
Edit edit: I do fully have dyscalcus, mostly only effects "scary" looking maths, so no, your suggestion doesn't help
Tbh, the last sentence was just a silly jab at the imperial units.
I was mostly just making fun of the fact that you implied the Fibonacci sequence can be memorized, when it is infinite. I'm not saying that referring to it is simpler than dividing/multiplying by a constant, no.
5 to 8 is the far simpler pretty exact conversion.