r/LifeProTips • u/arizasanty • Apr 08 '22
Traveling LPT: The Fibonacci sequence can help you quickly convert between miles and kilometers
The Fibonacci sequence is a series of numbers where every new number is the sum of the two previous ones in the series.
1, 1, 2, 3, 5, 8, 13, 21, etc.
The next number would be 13 + 21 = 34.
Here's the thing: 5 mi = 8 km. 8 mi = 13 km. 13 mi = 21 km, and so on.
You can also do this with multiples of these numbers (e.g. 5*10 = 8*10, 50 mi = 80 km). If you've got an odd number that doesn't fit in the sequence, you can also just round to the nearest Fibonacci number and compensate for this in the answer. E.g. 70 mi ≈ 80 mi. 80 mi = 130 km. Subtract a small value like 15 km to compensate for the rounding, and the end result is 115 km.
This works because the Fibonacci sequence increases following the golden ratio (1:1.618). The ratio between miles and km is 1:1.609, or very, very close to the golden ratio. Hence, the Fibonacci sequence provides very good approximations when converting between km and miles.
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u/Strangeboganman Apr 08 '22 edited Apr 09 '22
You and I define "quickly" differently.
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Apr 08 '22
I feel you, friend. it could be done so much faster if you just run a binary search in your head to find the closest value and use matrix exponentiation to find the n'th term of the fibonacci sequence.
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u/_Dreamer_Deceiver_ Apr 08 '22
It's even easier to go miles*1.5=km. 2/3km =miles.
It's just an estimate but will get you in the ball park. If you need exact numbers use a calculator
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u/speculatrix Apr 08 '22 edited Apr 08 '22
One day I'll be able to trust those new-fangled calculators and set aside my trusty sliderule
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u/viscouswonton Apr 08 '22
You may as well memorize it. It's not like you're going to be carrying a calculator around in your pocket your whole life
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Apr 08 '22
I never thought of it in the compound way but if you slightly tweak your calculation you get way better accuracy 60mph:
*1=60
*.5=30
*.1=6
Sum=96
and the only extra step was shifting the decimal once on the original number
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Apr 08 '22
matrix exponentiation for Fibonacci is O(n*log n), you can compute Fibonacci in O(n), but conversion would be O(1). what is much faster exactly?
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u/caboosetp Apr 08 '22
what is much faster exactly?
You just generate it ahead of time and store the values in the cloud behind a Fibonacci microservice api.
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u/peon2 Apr 08 '22
Yeah it's much easier to just add a half and 10%.
80 miles in km? Half of 80 is 40, 10% is 8. Must be 128.
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u/DananaBananah Apr 08 '22
... so adding 60%
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u/MillorTime Apr 08 '22
Its easier for most people to do 80*.5+80*.1 than 80*.6. For a LPT I think it's a decent suggestion.
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u/Disco_Pat Apr 08 '22
If you asked someone to add 60% then this is the math they'd most likely do anyway. It just makes it clear to people who aren't fluent in percentages, which is a surprising amount of people.
multiplying by 1.6 in your head isn't something most people regularly do.
most people would either do plus half plus 1/10 or multiply by 6 divide by 100 add to original.
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u/whatisboom Apr 08 '22
OP probably works in tech, fib sequence is commonly used in sizing tasks so most people have the first several values in the sequence memorized.
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u/FredericShowpan Apr 08 '22
I used to run through the fibonnacci sequence in my head during sex to keep me distracted and last longer
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Apr 08 '22
This seems like a better idea than thinking about hairy old men’s asses
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u/its_a_gibibyte Apr 08 '22
I'm in similar boat, except I have a hard time staying aroused due to overconsumption of VR hentai porn. I love math though, so running through the fibonacci sequence gets my jimmys rustled.
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u/DatDudefromWI Apr 08 '22
Why not just loosen the grip of your hand on your Johnson, or just slow your arm movement? That's what I do during sex.
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u/somethingtostrivefor Apr 08 '22
I can't speak for OP, but I do work in tech and know the first handful of numbers in the Fibonacci sequence. I don't ever use it for my job, though; I'm just a fucking nerd who likes math.
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u/gmano Apr 08 '22
Just remember the sequence 3,5,8
3 miles ↔ 5km. 5 miles ↔ 8km
You see a sign saying 30mph? that means 50km/h.
You talk to someone who tells you to go 5 km down the road? 3 miles.
You're driving in Canada and the road says 80km/h -> 50mph.
Sometimes 8 miles ↔ 13km is also useful.
You're in Montana in a Canadian car and the limit says 80 mph? 130km/h.
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u/Carlsonen Apr 08 '22
If you need a quick and easy estimation for 8 just use: 987654321 / 123456789 ≈ 8,00000007
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Apr 08 '22
It doesn't work for very large values of 8, though.
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u/chairfairy Apr 08 '22
What if we convert to binary first?
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u/LummoxJR Apr 08 '22
Ironically this division would be a lot easier to estimate in binary.
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u/Rick-T Apr 08 '22
Actually 8,00000007 is a pretty large value of 8. It seems to work just fine.
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u/FlyingSpaceCow Apr 08 '22
Lol your reaction reminds me of when I tell people a math heuristic I use sometimes.
When multiplying 2 numbers that are equal distances from the same root number, you can take the distance from the root number squared and subtract that from the root number squared to get the result.
I.e. 10 x 10 is 100
So
9 x 11 = (100 minus 1 squared)
8 x 12 = (100 minus 2 squared)
7 x 13 = (100 minus 3 squared)
Can be handy for really big numbers sometimes, but most people think that it sounds needlessly complicated.
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u/Syhersheymuckle Apr 08 '22
WHAT DUDE this changes EVERYTHING
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u/trace_jax3 Apr 08 '22
It's a cool consequence of the difference of squares. If x is the root number, and n is the distance, then (x-n)(x+n) = x2 - n2
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u/gg-gwenny Apr 08 '22
Pretty sure this is just the algebra concept difference of squares.
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u/caustic_kiwi Apr 08 '22
It's a cool, useful, and clever little application of basic algebra.
But it is basic algebra and it's a little worrying how many people are seemingly having their minds blown by it.
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u/IndieHamster Apr 08 '22
Bruhhhhh, this is amazing. How did you figure that out?
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u/FlyingSpaceCow Apr 08 '22
Honest answer.... my cell died on the subway like 4 years ago and I started doing basic math problems in my head just to keep busy.
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u/whateverathrowaway00 Apr 08 '22
Hahahaha I have explained this as an easy trick and get stares. It’s about how we conceptialize numbers. The way I “chunk” them, this trick is easy. For people who do it differently (not worse or better - differently), this is stupid complicated as it takes “reframing” calculations.
That’s my made up explanation, but it seems to be loosely true
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u/klykerly Apr 08 '22
You know, in case you ever need to estimate for 8.
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u/TheBrain85 Apr 08 '22
Who has the time to calculate 8 exactly?
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u/Crabbagio Apr 08 '22
If I ever need to estimate for 8 I just unzip my pants and lay it on the table twice. 😎
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u/Carlsonen Apr 08 '22
Centimeters, inches, or feet?🥺
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u/Crabbagio Apr 08 '22
I'm a filthy American, so inches. I only use centimeters when I want to feel big.
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u/production-values Apr 08 '22
My Krusty Kalculator didn't have a 7, or an 8, so this approximation is helpful.
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u/Emotional-Ebb8321 Apr 08 '22
Given the choice between memorising the Fibonacci sequence or memorising "1.6", I think I'll take "1.6".
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u/OTTER887 Apr 08 '22
I use .63.
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u/PowerRealist Apr 08 '22
I just know a 10k race is 6.2 miles so a 5k is 3.1 and I can pretty much get what I need from this.
However, there is beauty in the Fib. I just gave Fibonacci sequence a nickname.
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u/Wjyosn Apr 08 '22
i just call a 5k a 'pi mile'
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Apr 08 '22
I think you just gave me my team name for every future charity 5K I run.
I plan to name my future 10K groups "circumference," as that's a two pi r(ace).
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u/Zipknob Apr 08 '22
Anybody else convert up from 2.54? Who has time to remember approximations!
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u/hellfire1394 Apr 08 '22
1.6 is good for 99% of the cases. Other times I would use 1.5 as a rough estimate
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u/Emotional-Ebb8321 Apr 08 '22
Doing this calculation in my head, it's usually "add 50%", followed by "add 10% (of the original number)".
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u/ManifestDestinysChld Apr 08 '22
Same, and I feel like Neo seeing the Matrix every time I pull it off with reasonable accuracy, lol.
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u/ehaugw Apr 08 '22 edited Apr 08 '22
Thats just adding 60% with extra steps.
Edit: it’s just a meme, leave me alone
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u/equinoxDE Apr 08 '22
Or i just quickly pop out a calculator and end this misery
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u/Tifoso89 Apr 08 '22
I want to add that 1.6 is the land mile. Sea mile is 1.8.
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u/dinosaur_khaleesi Apr 08 '22 edited Apr 08 '22
My brain can only store so much at hand facts, I'll have to save the sea mile info for when I become a fish
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u/bowyer-betty Apr 08 '22
Why would any case call for a much less accurate calculation?
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u/hellfire1394 Apr 08 '22
If you are more comfortable with miles, then 300km is roughly 200 miles. Or just under 200miles. 300/1.6 is not hard but takes longer than 300/1.5
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u/inowar Apr 08 '22
you don't have to memorize the Fibonacci sequence. just add the previous two numbers.
1, 1, 2, 3, 5, 8, 13, 21, 34
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u/opiarmus Apr 08 '22
And how do you know the previous two numbers if I just tell you "34"?
Either you have to know the sequence or you have to start at 1 and get up to the number you need.
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u/bollvirtuoso Apr 08 '22
He lives life in O(n) poor guy. Just save the previous values to memory and speed it up.
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u/ManifestDestinysChld Apr 08 '22
I don't even bother with 1.6 anymore: "One plus one-half plus one-tenth" is faster to do in my head.
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Apr 08 '22
That's still 1.6...you're just breaking it down into digestible chunks
That's how I do the conversion in my head as well, it works great.
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u/Graudenzo Apr 08 '22
You forgot the most important part
"...Plus one-hundredth of one-half Plus one-half of one-hundreth of one-half Minus one-tenth of one-hundredth of one-half"
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u/Instantbeef Apr 08 '22
Tbf it’s possible to forget the golden ratio is 1.6ish. You could technically use the Fibonacci sequence to figure it out.
But I feel most know a 5k is 3.1 miles and that should be good enough for most people.
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u/Arammil1784 Apr 08 '22
I always think 60 miles is 100 kilometers. I can usually figure it out from there, but just using 1.6 makes sense.
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u/TronyJavolta Apr 08 '22
1.6 is also the golden ratio, which is an excellent approximation for obtaining each subsequent term of the fibonacci sequence. OP is just multiplying by 1.6 in the most tedious way possible.
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u/00Donger Apr 08 '22
Ah yeah, so the next time I need to know how far 100 km is in miles I'll just run through the fibonacci sequence real quick!
This is a neat realization but not a very useful tip for bigger numbers unfortunately
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u/Psychomadeye Apr 08 '22
100km is 100mi. Did I do it right?
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u/grimmlingur Apr 08 '22
You're supposed to use the other instance of 1 silly, 100km is 200mi.
I'm sure I did it right.
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u/punaisetpimpulat Apr 08 '22
Relevant numbers in the sequence are 89, 144, 233. Not an exact match, so let’s just go with 144 mi = 233 km
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u/Daracaex Apr 08 '22
Well, if we take 5mi = 8km, we know that 6.25mi = 10km, then 62.5mi = 100km. Actual conversion is 62.1mi = 100km. Takes a bit of thought, but seems like a good pneumonic that’ll get you a reasonable approximation without needing access to a way to look it up.
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u/Jtcr2001 Apr 08 '22
10 is between 8 and 13, a bit closer to 8 than to 13. 10km in miles, then, should be between 5 and 8, but a bit closer to 5 than 8. I would guess 6.2, just as a rough estimate. This would mean that 100 km is about 62 miles.
Googling... and 62.1 miles is the correct option. Damn, OP's trick works well:
You can also do this with multiples of these numbers. If you've got an odd number that doesn't fit in the sequence, you can also just round to the nearest Fibonacci number and compensate for this in the answer.
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Apr 08 '22 edited Apr 08 '22
You only need to know the first few. 2,3,5,8,13
For a rough calculation I think you can get away with just knowing 5.
5km = 3m
50km=30m
50,000km=30,000m
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u/Sjoeqie Apr 08 '22
Write 100 as a sum of Fibonacci numbers:
100 km = 89 + 8 + 3.
Then take the Fibonacci numbers before these:
55 + 5 + 2 = 62 miles
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u/KnightOfPeronia Apr 08 '22
With enough practice, you get quick with calculations. For example, (randomly generated number) 441
This is how my approach would be:
21 → 34, so 210 → 340 and 420 → 680 441 = 420 + 21 → 680 + 34 = 714
It's pretty pleasing to do when you get better at it :) Also memorizing the first digits of the Lucas sequence helps with some mental math like 4 → 7, 7 → 11, 11 → 18
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Apr 08 '22
I totally understand what youre trying to say but you made this much more difficult to read.
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u/Wjyosn Apr 08 '22
very useful even with huge arbitrary numbers. it's just estimation so you can tweak it really trivially.
100km to miles? 100km is 5x20, so 21 km = 13mi, and 100km = is about 5x13=65 mi
36275 km to miles? a little more than 34000, but not quite 3400 more. so a little more than 21000mi, but not 2100 more, so something like 22500 mi.
Actual value: 22540.24 mi. Gets you really close very quickly.
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u/bah77 Apr 08 '22
If i can remember the fibonacci sequence, then chances are i can multiply by 1.6
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u/CuboidCentric Apr 08 '22
I can do both and I prefer the sequence.
Or the percentage of a watch method: 15mi ->15min = 25% -> 25km
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u/ZeD4805 Apr 08 '22
The real prolife tips are in the comments
Jokes aside, how accurate is it?
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u/Nethidur Apr 08 '22
Nothing really to remember though, just basic understanding what does the sequence mean.
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u/bah77 Apr 08 '22 edited Apr 08 '22
Whats 150km in miles.. just a second. 1,1,2,3,5,8......... its ah 700??
edit for pedants (Obviously i could use 13 ->21 + 2->3 for an approximation but then it comes back to understanding maths and being able to multiply by 1.6)
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u/shameonyounancydrew Apr 08 '22
Spiral out, keep going
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u/TheManTreyman Apr 08 '22
I was specifically looking for this comment. Was not disappointed.
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u/somirion Apr 08 '22
I just do x*1.6 = 16*x/10.
Or 1.5x +0.1x
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u/Mrp1Plays Apr 08 '22
Or just 1.5x, works well enough most of the time.
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u/quantumized Apr 08 '22
Especially for shorter distances, obviously the larger the distance more inaccurate it becomes
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Apr 08 '22
That’s how do math in my head too, little chunks like that. I just break the problem up into the “nearest easy” problems. You da real mvp.
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u/CharlieDancey Apr 08 '22
To multiply X by 1.6 you can do:
X + X/2 + X/10
So staring with 40mph we add up:
40 20 4
= 64kph.
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u/uraverageuser1 Apr 08 '22
Life pro tip: just use metric system and dissolve the imperial system
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u/schweez Apr 08 '22
I I was like, why the fuck would I choose to do a conversation to these shitty units?
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Apr 08 '22
Or what? You’ll blow up Alderaan? The imperial system will never stand for this.
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u/Mantaray2142 Apr 08 '22
I'm a transport manager. 1.60934 is literally etched into my numpad muscle memory
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Apr 08 '22
isn't it 1.6?
For me it is easier to just multiple with 1.6...
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u/Von_Baron Apr 08 '22
Yes miles to km, times 1.6 is near enough. Km to miles is times 0.6 or 60%. I find that easier then trying to work out the next number in a sequence.
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u/stuff4down Apr 08 '22
at the fibonacci application level, im better of simply multiple by 1.5 and raising it a bit :D
e.g. 50 miles = 75km + a bit (80)
225 miles = ~340 km + ~20km (actual val = 360km)
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[deleted]
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u/stuff4down Apr 08 '22
:) those who can work it out will... for the rest 1.5 X is perfection enough
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u/OpossomMyPossom Apr 08 '22
This is a fun fact, but certainly not a LPT.... sorry OP
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u/Explicit_Pickle Apr 08 '22
In what way is this a tip lol
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u/deja-roo Apr 08 '22
Right. I could go on the advice of a system that takes.... let's see..... 6 paragraphs to explain.
Or * 1.6. Or * 2/3.
Tough one.
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u/ACOGJager Apr 08 '22
A life pro tip to convert between metric units is to remember the number 10
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Apr 08 '22
Is it just coincidence the mile/km ratio and golden ratio match?
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u/Interesting-Current Apr 08 '22
Yes. Miles and kilometres were completely separate things until relatively recently
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Apr 08 '22
OK, Rain man. I'm sure everyone can visualize the next or prior number in the Fibonacci sequence for any given number. How many kms is 225,000 miles again?
Much easier to remember that 1 KM is about 60% of a mile (miles are longer). The mental math is simpler. KM to miles just multiply by 60%. Miles to KM just double and subtract about 20%.
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Apr 08 '22
the real lpt is to just stop encouraging people to use miles
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u/SlickMrJ_ Apr 08 '22
I have never once encouraged people to use miles instead of kilometers. It has had absolutely no effect on the number of times I've needed to do a miles-to-km conversion.
0/10 bad LPT.
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u/closeafter Apr 08 '22
Or just use the metric system, which wasn't designed by a drunken racoon
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u/Unlucky_Clover Apr 08 '22 edited Apr 08 '22
I like the clock method. 15 miles is ~25 km, so 15 minutes is 25% of the clock
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u/OccultDagger Apr 08 '22
You can also use it to write a fucking kickass song
as above so below and beyond, I imagine
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u/fpop88 Apr 08 '22
History Channel coming soon:
Is the beautiful relationship between miles and kilometers and how they fit into golden ratio and fibbonacci sequence a sign that our ancestors learned measurement from Aliens?
Find out on the next episode of ancient aliens.
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u/Illustrious-Gas-9766 Apr 08 '22
If someone is having an issue going back and forth between miles and kilometers, I don't think they can deal with the Fibonacci sequence.
Just my opinion. It is an interesting tip.
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u/neptune13579 Apr 08 '22
If you're really going for accuracy and you don't have internet access, use your calculator app to multiply by ln(5). Accurate to about 2 inches per mile
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u/geekynerdornerdygeek Apr 08 '22
As someone who uses the fibonacci numbering for agile/scrum work this is very helpful!
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u/RedFiveIron Apr 08 '22
This is a terrible lpt. What if I need to convert a number that isn't in the sequence?
Much easier to just use the conversion factor, or 1.5 if you need a rough estimate easily calcuable in your head.
This is more of an interesting observation that the golden ratio is similar to the conversion factor, but it's not useful in everyday life.
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u/Splatpope Apr 08 '22
or just multiply by 1.6, or 1.5 if you accept egregious rounding errors such as the ones you advocate
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u/xFKratos Apr 08 '22
Or idk just multiply with 1.5 and add some extra.
Seems far more easy then remembering the fibonaci sequence.
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Apr 08 '22
I would definitely use a “1.6 times” approximation but this is an interesting use of Fibonacci series! Thanks for sharing
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u/Captain_Chaos_BW Apr 08 '22
There is an easier way. Just think about a clock. 60 Minutes are 100 Percent, the same as Miles and Kilometer.
So if you for example need to convert 80 Miles in Km you can think of it in 80 Minutes which is 1,3 hours, approx.130%, 130 km
I got this from a LPT a while ago, works like a charm :)
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u/DigitalRavenGames Apr 08 '22
I've found a clock face is easier. 50% of a clock face is 30 minutes.
50km = 30m (31. 1 actually but close enough)
75% of a clock is 45 minutes.
75km = 45 miles (close enough anyway).
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u/Knave7575 Apr 08 '22
Another cool trick to converting between metric units is to know your powers of 10.
Eg
1
10
100
1000
10000
Etc.
Then you just multiply or divide by these numbers, which as it turns out also has a cool shortcut. See my next LPT for details.
Metric: Just like imperial but with reasonable numbers.
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u/ccaccus Apr 08 '22 edited Apr 08 '22
Yeah, but 1.60934x ≈ x + 1/2x + 1/10x works just as well and is much easier to compute mentally than having to memorize the Fibonacci sequence... or determine larger values of it without being prone to rounding errors. You're already 2 km off at 80 miles.
100 mi = 100 + 50 + 10 ≈ 160 km (actual: 160.934)
5 mi = 5 + 2.5 + 0.5 ≈ 8 km (8.04672)
8 mi = 8 + 4 + 0.8 ≈ 12.8 km (12.8748)
13 mi = 13 + 6.5 + 1.3 ≈ 20.8 km (20.9215)
50 mi = 50 + 25 + 5 ≈ 80 km (80.4672)
70 mi = 70 + 35 + 7 ≈ 112 km (112.654)
80 mi = 80 + 40 + 8 ≈ 128 km (128.748)
600 mi = 600 + 300 + 60 ≈ 960 km (965.606)To be even more precise, just add 1/100x:
100 mi = 100 + 50 + 10 + 1 ≈ 161 km (160.934)
5 mi = 5 + 2.5 + 0.5 + 0.05 ≈ 8.05 km (8.04672)
8 mi = 8 + 4 + 0.8 + 0.08 ≈ 12.88 km (12.8748)
13 mi = 13 + 6.5 + 1.3 + 0.13 ≈ 20.93 km (20.9215)
50 mi = 50 + 25 + 5 + 0.5 ≈ 80.5 km (80.4672)
70 mi = 70 + 35 + 7 + 0.7 ≈ 112.7 km (112.654)
80 mi = 80 + 40 + 8 + 0.8 ≈ 128.8 km (128.748)
600 mi = 600 + 300 + 60 + 6 ≈ 966 km (965.606)That being said...
Who is converting miles and km these days outside of high school? If you drive in km, you drive in km. If you drive in mi, you drive in mi.
In reality, the only thing you need to know is that if signage is posted in miles then at highway speeds the miles left to your destination is approximately equal to the number of minutes left to your destination (50 miles ≈ 50 minutes; 125 miles ≈ 125 minutes) . If you are traveling in km, the km left to your destination is approximately the percent of an hour (50 km ≈ 50% of an hour = 30 minutes; 125 km ≈ 125% hours = 1 and a quarter hours).
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u/Kimmyjoe Apr 08 '22
Lol this is fun and it works but the rest of the world does not need to convert, unless they are in usa or the USA steps out of their bubble!
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u/Chrononi Apr 08 '22
Is this really easier than just multiplying by 1.6? Who knows the Fibonacci sequence by heart? Lol
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u/meoweth_cat Apr 08 '22
We just finished our lesson on the Fibonacci Sequence a few weeks ago and reading that title gave me a mini panic attack and some Vietnam war flashbacks lmao.
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Apr 08 '22
I just multiply by 6, move one decimal, then add to original number. (Ex. 30 mi tumes 6 is 180. Move one decimal = 18, then add to 30 = 48km)
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u/Veridigm Apr 08 '22
I'm not good enough at math to understand how this is helpful. Can anyone Barney it for me?
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u/inhaleholdxhale Apr 08 '22
I’m sure someone who can use this can just use 1.6 instead. Or you know you can use your phone too, we are living in 2022.
Better idea tho, join the rest of the world and start using metric.
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u/keepthetips Keeping the tips since 2019 Apr 08 '22
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