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Converting miles to kilometers using fibonacci numbers

ricitosdeplata

Active Member
Time of past OR future Camino
09/2015: Via de la Plata
It's been slow going to have to multiply and divide to figure out how many km there are in a distance in miles and vice versa. When I was using Google to convert I ran into a quicker way by using fibonacci numbers. These are the sequence of numbers that you get by ading two adjacent numbers. Starting with 0, add 1. This gives you 0,1,1. Add 1 and 1, you get 2, for the sequence 0,1,1,2. Repeating this your sequence is then 0,1,1,2,3,5,8,13,21,34,55 etc.

If you want to convert 5 miles into km, look at the number to the right to see that it's 8 km. Or you could see that 34 km is 21 miles. This system is approximate, but it's a quick way to figure out distances.

For most of the world, kms aren't a problem. Maybe if one of the U.S. presidential hopefuls wins, might change.
Here's the link and further explanation of how to figure numbers not on this sequence:
http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-miles-to-kilometers/
 
The 2024 Camino guides will be coming out little by little. Here is a collection of the ones that are out so far.
It's been slow going to have to multiply and divide to figure out how many km there are in a distance in miles and vice versa. When I was using Google to convert I ran into a quicker way by using fibonacci numbers. These are the sequence of numbers that you get by ading two adjacent numbers. Starting with 0, add 1. This gives you 0,1,1. Add 1 and 1, you get 2, for the sequence 0,1,1,2. Repeating this your sequence is then 0,1,1,2,3,5,8,13,21,34,55 etc.

If you want to convert 5 miles into km, look at the number to the right to see that it's 8 km. Or you could see that 34 km is 21 miles. This system is approximate, but it's a quick way to figure out distances.

For most of the world, kms aren't a problem. Maybe if one of the U.S. presidential hopefuls wins, might change.
Here's the link and further explanation of how to figure numbers not on this sequence:
http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-miles-to-kilometers/
Interesting. I did not know this. It doesn't look like it would be as quick as my converter app, but it would certainly be more fun to play with.
 
For those who find conversion tricky, here's an idea I use for currency conversion.

When shopping overseas I usually carry a simple conversion table.

I make it on a spreadsheet and print it the size of a credit card. Then once printed I laminate it.

So you end up with a 'credit card' sized conversion table. You can fit about 50 figures on each side.

So for example you could do miles to km on one side and km to miles on the other.

Just a thought....
 
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well, I normally use these references

5 miles = 8 km
10 km = 6 miles

it works reasonably well, I hope the USA finally adopt the decimal measurement system...
 
I can keep .6 in my head and multiply or divide by it. Calculating a Fibonacci number in my head is no longer within my capabilities (ex-math major). My iPhone calculator can give me decimals if I need them, and there are applications for both kilometer and Euro conversion.

Fibonacci Day is November 23 (for a reason). :)
 
For those who find conversion tricky, here's an idea I use for currency conversion.

When shopping overseas I usually carry a simple conversion table.

I make it on a spreadsheet and print it the size of a credit card. Then once printed I laminate it.

So you end up with a 'credit card' sized conversion table. You can fit about 50 figures on each side.

So for example you could do miles to km on one side and km to miles on the other.

Just a thought....
That's what I do with liters and gallons as I drive in and out of the U.S. and Canada. My little card helps me keep up with mpg.
 
Down bag (90/10 duvet) of 700 fills with 180 g (6.34 ounces) of filling. Mummy-shaped structure, ideal when you are looking for lightness with great heating performance.

€149,-
I can keep .6 in my head and multiply or divide by it. Calculating a Fibonacci number in my head is no longer within my capabilities (ex-math major). My iPhone calculator can give me decimals if I need them, and there are applications for both kilometer and Euro conversion.

Fibonacci Day is November 23 (for a reason). :)
Would you mind explaining the reason.....has gone completely over my head....:rolleyes:o_O
 
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It's been slow going to have to multiply and divide to figure out how many km there are in a distance in miles and vice versa. When I was using Google to convert I ran into a quicker way by using fibonacci numbers. These are the sequence of numbers that you get by ading two adjacent numbers. Starting with 0, add 1. This gives you 0,1,1. Add 1 and 1, you get 2, for the sequence 0,1,1,2. Repeating this your sequence is then 0,1,1,2,3,5,8,13,21,34,55 etc.

If you want to convert 5 miles into km, look at the number to the right to see that it's 8 km. Or you could see that 34 km is 21 miles. This system is approximate, but it's a quick way to figure out distances.

For most of the world, kms aren't a problem. Maybe if one of the U.S. presidential hopefuls wins, might change.
Here's the link and further explanation of how to figure numbers not on this sequence:
http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-miles-to-kilometers/

An interesting but not so simple conversion process. Thank you for sharing.

That said, I am not sure why conversion matters while walking in Europe. The phrase "When in Rome" comes to mind. A rough, simple calculation would be to multiply the Km's times .6 if you need to know how many miles.

In regards to the U.S. converting to the metric system, we have been down this road before. Unlikely to happen in our lifetime. I personally would find it much more helpful to have a common world currency or language. No matter the language or currency.

Ultreya,
Joe
 
Although I speak both English and American, there are a lot of people around the world where this would not be so obvious. They will wonder why 23/11/15 should be celebrated.
With my newly acquired knowledge.....1,1,2,3, the year is not significant.
 
The one from Galicia (the round) and the one from Castilla & Leon. Individually numbered and made by the same people that make the ones you see on your walk.
An interesting but not so simple conversion process. Thank you for sharing.

That said, I am not sure why conversion matters while walking in Europe. The phrase "When in Rome" comes to mind. A rough, simple calculation would be to multiply the Km's times .6 if you need to know how many miles.

In regards to the U.S. converting to the metric system, we have been down this road before. Unlikely to happen in our lifetime. I personally would find it much more helpful to have a common world currency or language. No matter the language or currency.

Ultreya,
Joe
Single currency is not working out too well in Euro zone.....I believe....
 
A pound is a pound the world around just like a meter is a meter... and it is equal to a normal human's pace, one pace times a 1000 paces equals one kilometer. Unless you have a shorter pace like me and therefore about 1300 paces makes a kilometer for me which I can usually cover in about 20 minutes per hour or less on a good day.
Currency conversion is best left to your ATM, last month it was 1.05 euros to the USD, today it is 1.15!
The fun math to do in your head is the conversion of the price one pays for European petrol versus US gasoline. It requires converting litres to gallons and then a currency conversion, the best I can say I am paying about $8 per gallon, but what the hell I need to drive my car so I pay for it anyway.
 
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Far better than switching from Lira to Drachma to Franc's etc. etc. etc. like it used to be pre Euro.
Guess there will always be an up and a down side.
 
Down bag (90/10 duvet) of 700 fills with 180 g (6.34 ounces) of filling. Mummy-shaped structure, ideal when you are looking for lightness with great heating performance.

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I grew up learning miles and kilometers. I learned that if you hold out your arms the distance between your hands is that much regardless of whether its measured in meters, feet, or cubits.
 
I grew up learning miles and kilometers. I learned that if you hold out your arms the distance between your hands is that much regardless of whether its measured in meters, feet, or cubits.

Cubit an old form of measurement from a person's elbow to the tip of their middle finger. A distance of 18 to 21 inches or roughly 46 to 53 cm's, if I recall.
 
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The 2024 Camino guides will be coming out little by little. Here is a collection of the ones that are out so far.
My point was that most of the world will not recognise that date as part of the Fibonacci sequence since the vast majority write the 23rd of November as 23/11.
Lots of things go over my head.....
My point was that most of the world will not recognise that date as part of the Fibonacci sequence since the vast majority write the 23rd of November as 23/11.
Sorry...lots of things go over my head..........:rolleyes:..o_O
 
My point was that most of the world will not recognize that date as part of the Fibonacci sequence
It is not an internationally recognized day!! :) You may have missed the insouciant air of U.S. chauvinism in picking the date...

Pi Day is on Albert Einstein's birthday (or the first day of apple harvest). :confused:
 
A pound is a pound the world around just like a meter is a meter... and it is equal to a normal human's pace, one pace times a 1000 paces equals one kilometer. Unless you have a shorter pace like me and therefore about 1300 paces makes a kilometer for me .
A thousand paces per km is another interesting factoid. Either I have even a shorter pace or I'm dawdling. According to my Fitbit (and its results are admittedly questionable) I average 1492 steps per km.
 
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It is not an internationally recognized day!! :) You may have missed the insouciant air of U.S. chauvinism in picking the date...

Pi Day is on Albert Einstein's birthday (or the first day of apple harvest). :confused:
First Apple picking day in US or elsewhere....are we in danger of going of thread here.....unless we can incorporate Apple's into conversion of miles to kilometres.....:mad:o_O
 
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It is not an internationally recognized day!! :) You may have missed the insouciant air of U.S. chauvinism in picking the date...

Pi Day is on Albert Einstein's birthday (or the first day of apple harvest). :confused:
Pi day is next Tuesday at the pub.....hmmmm lovely...
 
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Whoa!! Surprised by the number of responses. Maybe Lincoln Chaffee is on to something.

This conversion has nothing to do with dates. I feel my leg being pulled.

I'm usually trying to convert kilometers to miles or vice versa when I'm walking and I don't pull out my cell phone to check. I think the brain usually wants to relate new information to what we already know. As I try to increase my distance I want to know if I'm getting close to what I need to be able to walk easily and that's listed in guide books in km. Maybe after walking almost 1000 km on Vdlp I'll have a physical sense of what a km means.

Inclined not to use .6, and instead use .6214, because I want to get credit for every step.
 
@ricitosdeplata, I get your meaning that you like to convert new info to something you are used too as I do too BUT on the Camino the new quickly becomes the familiar as the guidebooks, signs, just everything is in km. Therefore if you want to know miles as a way to recognize your comfort zone you would have to convert the signs, etc as well. It truly is easier to use what is in front of you as you journey. Now if you want to convert to miles to share with your loved ones back home, that's another story, but it can be done outside of real time. Just my thoughts on the matter----aka "what I do". :)
 
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A thousand paces per km is another interesting factoid. Either I have even a shorter pace or I'm dawdling. According to my Fitbit (and its results are admittedly questionable) I average 1492 steps per km.

I usually lose count around 400 steps. It doesn't matter ... I'm going to walk that km whether or not it takes 1000 steps or 1492 steps. And another ... until I get there.
 
Let's step back a second - why do we care about converting km to miles or visa versa? If you're walking in a metric country, just use km. Who cares how many miles that is?
 
K I just don't understand why you don't take the 800 km and learn what a KM is. The idea of learning something new is relating it to your person not former understanding. Thats like trying to figure out Canadian vs American football and then trying to relate it to what the rest of the world knows as football which is soccer for Canadians and Americans. It just isn't going to make sense. I am currently learning Spanish. I can't relate it to Canadian English because it doesn't relate. I end up thinking french and then get all screwed up so I am just immersing myself with spanish...forget trying to relate it...eventually it comes to us. I dunno ...thats just me...??
 
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My Dad was a math teacher and the one thing he taught me that I always remember is to convert miles to Km and vice versa

Miles to KM is simply multiply the number by 8 the divide by 5

eg 60 miles * 8 divide by 5 = 96km
(most people round it and say 60 = 100)

Km to miles is the other way around multiply by 5 and divide by 8

eg 100 kms *5 divide by 8 = 62.5
 
Would you mind explaining the reason.....has gone completely over my head....:rolleyes:o_O
One learns something new every day. I too goggled this and discovered that November 23 is known as Fibonacci because the first numbers of the Fibonacci Series are 1, 1, 2, 3, and the Fibonacci sequence adds the previous 2 numbers to get the third. Although I take @MichaelSG 's point about the American Vs the English way of writing the date!.
Suzanne :)
 
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Although British born and bred, I've used the metric system since I left Britain at the tender age of 21. However, I still find myself saying things like "you won't get much mileage out of that....", or "..that's miles away from where I'm living/working...". And at 61 years of age, I don't see me ever changing that phraseology!!!
Suzanne :p
 
I still like my beer in imperial measure. A pint seems just right.
 
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Far better than switching from Lira to Drachma to Franc's etc. etc. etc. like it used to be pre Euro.
Lira were great. I remember going to an ATM in Italy before they went Euro. Withdrew a million Lira. I think it was about $600.00. I'd never been a millionaire before. The smallest coin or bill was 10, or 100 or something; when a price was not even you just rounded it off.
 
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Lira were great. I remember going to an ATM in Italy before they went Euro. Withdrew a million Lira. I think it was about $600.00. I'd never been a millionaire before. The smallest coin or bill was 10, or 100 or something; when a price was not even you just rounded it off.
I'm going thru that in Norway right now. The smallest is 50 so I'm rounding. I do not want a pocket of coins.
 
Marcristina, I thought you were kidding about the Irish mile, then I looked it up. The Irish mile 1440 feet longer!
 
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A year before I walked my camino I changed my FitBit and my iPod Nano over to km's and just started thinking that way. I know the km's for all my local training walks (and have them posted on the fridge for easy reference). What I can't figure out is why my local 10km walk over rolling hills up to a certain road and back, seems so short and 10km on the Frances seemed longer!
 
If you've been around for a while and always liked a bet on the horses, kms to miles is nothing. You can do metres to furlongs easy as 2 times tables.
 
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......and a "country mile" is longer than any other version.....;)

When I first started at University en route to becoming an architect we used Imperial for our designs/drawings; in second year we switched to metric so I am "bilingual" in both.

Of course the non-anthropometric metric system is all the fault of the French and their "bloody" revolution. However a few years ago I was measuring for alterations a farmhouse if France and as I wrote down the distances between and of windows I suddenly realised that the building was in Imperial feet and inches (4'0" then 3'0" then 3'6" and so on) and therefore must pre-date that revolution.

As to pints and gallons - beware the difference between the UK and the US as post the Yanks chucking tea into Boston harbour us Brits upped the pint to 20 fluid ounces whilst the Americans stuck to the old 16 fluid ounce pint.
 
Marcristina, I thought you were kidding about the Irish mile, then I looked it up. The Irish mile 1440 feet longer!
The Irish have nothing on the Scandinavians. I was surprised when walking St Olavs Way at one young Norseman who told me he was walking 3.5 miles a day. Later I found out I should have been more impressed!
 
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The Fibonacci km-miles conversion works coincidentally because the Fibonacci series approximates the Golden Ratio (1.618), which approximates the kilometer to miles conversion ratio (1.609). Other ratios also converge on the Golden Ratio, therefore can be used to approximate a conversion of kilometers to miles. Pick the two numbers before the conversion you want, and construct a Fibonacci-like series. Higher starting points take a little longer to converge.

3+4=7 Four miles is approximately 7 kilometers.
4+5=9 Five miles is approximately 9 km.
5+6=11 Six miles is approximately 11 km.
11+12=23 Twelve miles is approximately 23 km.

The Fibonacci spiral is not uniquely magical for the conversion.

I still find multiplying or dividing by .6 is easiest for me to retain in my synapses (when I care at all about converting, which is rarely)!!
 
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It's been slow going to have to multiply and divide to figure out how many km there are in a distance in miles and vice versa. When I was using Google to convert I ran into a quicker way by using fibonacci numbers. These are the sequence of numbers that you get by ading two adjacent numbers. Starting with 0, add 1. This gives you 0,1,1. Add 1 and 1, you get 2, for the sequence 0,1,1,2. Repeating this your sequence is then 0,1,1,2,3,5,8,13,21,34,55 etc.

If you want to convert 5 miles into km, look at the number to the right to see that it's 8 km. Or you could see that 34 km is 21 miles. This system is approximate, but it's a quick way to figure out distances.

For most of the world, kms aren't a problem. Maybe if one of the U.S. presidential hopefuls wins, might change.
Here's the link and further explanation of how to figure numbers not on this sequence:
http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-miles-to-kilometers/

I love this! Thanks for posting, Ricitosdeplata!
 
The one from Galicia (the round) and the one from Castilla & Leon. Individually numbered and made by the same people that make the ones you see on your walk.
I'm another one who tends to convert kms to minutes rather than miles. 1km = 11mins. I have a mobile device on my left wrist that allows me to measure my progress.
 
That's what I do with liters and gallons as I drive in and out of the U.S. and Canada. My little card helps me keep up with mpg.

Must have been tough when Canada used the gallon. Then you had to convert from Imperial to US
 
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That is all very interesting but what about Irish miles which are longer than English miles?
Another thing.......what of rods poles and perches??
I think some spanish kilometres were measured with very stretchy elastic....some of them seemed to go on for miles and miles
 
The Fibonacci km-miles conversion works coincidentally because the Fibonacci series approximates the Golden Ratio (1.618), which approximates the kilometer to miles conversion ratio (1.609). Other ratios also converge on the Golden Ratio, therefore can be used to approximate a conversion of kilometers to miles. Pick the two numbers before the conversion you want, and construct a Fibonacci-like series.

3+4=7 Four miles is approximately 7 kilometers.
4+5=9 Five miles is approximately 9 km.
5+6=11 Six miles is approximately 11 km.
11+12=23 Twelve miles is approximately 23 km.

The Fibonacci spiral is not uniquely magical for the conversion.

I still find multiplying or dividing by .6 is easiest for me to retain in my synapses (when I care at all about converting, which is rarely)!!
I really wish you had been my maths teacher ... you have explained that so well that even a numpty like me will remember it. Thank you
 
Nobody mentioned that last 0.9km before Lorca.
 
Down bag (90/10 duvet) of 700 fills with 180 g (6.34 ounces) of filling. Mummy-shaped structure, ideal when you are looking for lightness with great heating performance.

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I must admit to doing quick calculations by simple proportions and the two easy points to remember accurately. The points are 5mi=8km and 6mi=10km.

1 mi - 1/5 of 8000m = 1600m or 1.6km (although I probably just remember that which makes it three points!)
2 mi - double 1.6 = 3.2
3 mi - triple 1.6 = 4.8 km
etc
After 10 mi (double five or 16 km)
11mi - 5mi +6mi = 8km + 10km or 18km
12 mi - double 6 mi = 20 km
etc
 
Dougfitz, I have done some 5K and 10 K runs so multiples of these are easier for me to figure out. Using your 1.6 constant is a great idea that I'll add to my bag of tricks.
 
I think some spanish kilometres were measured with very stretchy elastic....some of them seemed to go on for miles and miles
I had that sensation in some parts of the way too... Sometimes thinking the next stone mark would be 1km down, and it was only 0.5!
 
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The mile was originally invented by the Romans, to whom it was 'mille passus', a thousand-pace. A pace was a double-step, left and right, of a Roman soldier. So it was meant to be decimal.
 
The mile was originally invented by the Romans, to whom it was 'mille passus', a thousand-pace. A pace was a double-step, left and right, of a Roman soldier. So it was meant to be decimal.
How interesting. I know that my pace length is about 82 cm, so I do just a bit less than 2000 steps / mile. It makes me wonder how tall Roman soldiers might have been to sustain an 80 cm pace. I generally have this image that people even a couple of centuries ago were generally much shorter than we are today, and it would have been difficult to have the same stride length we might be accustomed to in our everyday lives.
 
Like Dougfitz I use the 8km is 5mile/6miles is 10km approach and just multiple that up until it fits... When cycling I have miles set on my bike and my hubby has kilometres, then for months afterwards I can relive the journey by adding the daily numbers up and comparing them...! If i'd not lost my photos I might of had something better to do....
Really interesting that this too fits the Fibonacci numbers - as a gardener I take great delight in counting petals/flowers that grow in Fibonacci numbers and even made a shell mosaic to illustrate the fact... Again - I should get out more...
 
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The Fibonacci km-miles conversion works coincidentally because the Fibonacci series approximates the Golden Ratio (1.618), which approximates the kilometer to miles conversion ratio (1.609). Other ratios also converge on the Golden Ratio, therefore can be used to approximate a conversion of kilometers to miles. Pick the two numbers before the conversion you want, and construct a Fibonacci-like series.

3+4=7 Four miles is approximately 7 kilometers.
4+5=9 Five miles is approximately 9 km.
5+6=11 Six miles is approximately 11 km.
11+12=23 Twelve miles is approximately 23 km.

The Fibonacci spiral is not uniquely magical for the conversion.

I still find multiplying or dividing by .6 is easiest for me to retain in my synapses (when I care at all about converting, which is rarely)!!
I dont want to nit-pick but this method is pretty inaccurate.12 miles is actually 19.3 km's not 23 and worse still 50 miles is 80.46 km's and not,as per formula 99 km's. Or am I getting it completely wrong
Joe
 
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
Yep, this methods has its drawbacks. One thing, though, is that numbers, say like 90, aren't on the fibonacci series, so you have to take multiples or different fibonacci numbers to get your conversion.

An easy way to figure out 50 miles would be to use the adjacent f. numbers 5 and 8. Multiply 5 mile by 10, or 10 x 8 km for a product of approx. 80 km = 50 miles.

To figure out how many mile in 99 km, separate it out into 89 km + 5km + 5km = 55 mi. +3 mi + 3 mi = approx 61 miles.

(I've gotta get a life!)
 
I dont want to nit-pick but this method is pretty inaccurate.12 miles is actually 19.3 km's not 23 and worse still 50 miles is 80.46 km's and not,as per formula 99 km's. Or am I getting it completely wrong
Joe
@joeboybollo, if as a walker you are really worried about the accuracy of the larger numbers, I will take my hat off to you.
 
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well, I normally use these references: 5 miles = 8 km ; 10 km = 6 miles.
it works reasonably well, I hope the USA finally adopt the decimal measurement system...
I know we can all HOPE - we in Oz hope our current prime minister might learn about climate change - but as for the US and adopting the metric system, well with a 300 million domestic market they (consider) that they really have no need to change. Still we can all hope. cheers.
 
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