This is because fibonacci numbers approach golden ratio which is approximately 1,618033... and one mile is 1,609344 kilometres exactly.
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And yet the military uses "clicks"
0.54 nmi (nautical miles)
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.
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.
or add half and then 10% (because it’s 1.6km to the mile): easier than multiplying decimals or large numbers by 6, and the inverse is 0.6mi=1km so easy to remember both ways (same thing but don’t “add” just start from 0)
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".
Works because ratio of km to miles is about the golden 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
Neat!
Cool! I wish I would have known this in the 70's when Canada changed over from British Imperial units to the Metric system. Maybe this is the incentive needed to push the usa into the rest of the metric system world!
If every measurement being a factor of ten of a smaller or bigger unit isn't going to convince Americans of the ease of metric then the Fibonacci sequence isn't going to convince them.
What if i don't want to
That's the spirit.
Give it the ol college "why?"
5 to 8 is the far simpler pretty exact conversion.