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Shea Gunther

Cool math trick: Converting between miles and kilometers

Here's a very cool trick for using math to convert between miles and kilometers.

Tue, Aug 16 2011 at 11:28 PM EST
 93

Mileage sign Photo: Try Stan/Flickr
The Fibonacci sequence is made up of numbers that are the sum of the previous two numbers in the sequence, starting with 0 and 1.
 
It's 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
 
1 is 0+1, 2 is 1+1, 3 is 1+12, 5 is 2+3, and 8 is 3+5. The number after 144 is 233, or 89+144.
 
The Fibonacci number describes the golden spiral, an ideal form much beloved by designers everywhere. Interestingly, it also neatly matches the relationship between kilometers and miles. Three miles is five kilometers, five miles is eight kilometers, eight miles is 13 kilometers. It's not perfect, eight miles is actually 12.875 kilometers, but it's close enough in a pinch.
 
If you need to convert a number that's not on the Fibonacci sequence, you can just break out the Fibonacci numbers, convert, and add the answers. For instance, 100 can be broken down into 89 + 8 + 3, all Fibonacci numbers. The next numbers are 144, 13, and 5, which add up to 162. 100 miles is actually equal to 160.934. Again, close enough.
 
Math is cool.
 
Via Reddit
 
Edit: I made a typo on 1+1=3. Thanks to reader Erlinda for catching it.
 
Are you on Twitter? Follow me (@sheagunther) there, I give good tweets.
 
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anonymous
Tricky 05/21/2012 14:10 PM

I met a woman at a bar last night and told her this cool trick. She asked my number and later that night called me her home. Her sister, who was also at home, learnt this cool trick. and got really really wet. Needless to say, we had a threesome. Thank you. Math is sexy!!

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anonymous
jack sprat 05/19/2012 23:57 PM

The seeming relationship is interesting, but not practical. Easier to take km, triple, double, and move the decimal point one space to the left. Alternatively, add 2/3 to the mileage.

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anonymous
john 05/14/2012 19:10 PM

easier to just know the conversion and divide.

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anonymous
Alexi 05/05/2012 15:18 PM

The joys of pure mathematics. It only becomes interesting at points where it is ridiculously useless.

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anonymous
gianni sermon 04/28/2012 08:36 AM

Did you know that the distance between the leaves of a plant follow the Fibonacci's scale?

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anonymous
jack sprat 05/20/2012 00:15 AM

There's an animated film (in color), probably made by Disney in the late 1930s, which illustrates the Fibonacci sequence in nature. It's well-nigh universally present in life, often in surprising ways. It shows up in classical painting and seems to account for no small part of the emotional impact on the viewer. Its use serves to draw the eye through the painting as the artist intends. The same attraction holds in judging physiognomy for mating selection and in the related human notion of.... More

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anonymous
Andrew 04/27/2012 21:29 PM

You know how I convert? I look at the "km/h" scale on my speedometer. Whilst everyone else who is frantically trying to recall the memorized fibonacci sequence and break down non-fibonacci terms is running in to the cars in front of them.

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anonymous
MoMo 04/27/2012 13:37 PM

Multiply by .62 and you're done - why make this a chore?!
If you run a 10k everyone knows that's 6.2 miles...

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anonymous
kanvi 04/27/2012 05:49 AM

really its very cool

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anonymous
Rex Remes 03/24/2012 00:27 AM

Easiest trick is remember 0.6

From miles to km, add 0.6 more. 50 -> 50 + 30 = 80

From km to miles, multiply by 0.6. 80 -> 80 x 0.6 = 48

Easy-peasy and you are within 3%

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anonymous
Anonymous 03/07/2012 17:03 PM

I don't understand it.

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anonymous
AlfsDogs 04/24/2012 19:12 PM

It is not that I don't understand what was written, it is just that I would only go through all that mental or even on paper or electronic go through all those steps to get where I want to be with the final answer.

The presentation was a nice exercise in mental exploration for the lesser math buffs such as myself and a conversation piece for so many others.

There were some other tricks that came out here on metrics in measurement as the discussion also included conversions " C - F".... More

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anonymous
paul Today 12:57 PM

so I'm at a local bar last night and get into a conversation with a pretty little woman. I tell her about this conversion trick and next thing I know she's like wow and can't believe how cool I am. Next thing she is asking me to her place where she has a hot latina roommate and she is telling her friend about my math trick. lets just say I left with a smile from ear to ear

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anonymous
Enter your name 02/17/2012 15:27 PM

or you can just use the iphone app

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anonymous
Here's your card 02/04/2012 09:46 AM

seriously?? how pointless and dumb. If you need a proxy in a pinch as the article suggests (note his messy calculations don't even come up with the right answer), just use 1.5 as your base.

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anonymous
Frank 01/30/2012 01:01 AM

This is badly written, badly explained, and rather useless. It presupposes that you either have the fibonacci sequence memorized, or that you spend time trying to count it up in your head to the values you need. Anyone who can do that can just multiply or divide by 1.6 instead and be done with it. It's only a cool math trick if it makes things EASIER. This does nothing of the sort.

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anonymous
Anonymous 02/02/2012 01:46 AM

Curious. Didn't find this badly written, explained or useless. While I may not readily know the Fibonacci sequence out to the realm of 4 digit numbers, this method seems perfectly viable and helpful as a mnemonic for distances below 100.

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anonymous
Zippy the Wonder Slug 01/11/2012 21:25 PM

If you're enough of a geek to have the Fibonacci sequence memorized, you're enough of a geek to be able to manually multiply by 1.6.

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anonymous
Richard H 01/11/2012 07:54 AM

SAE is the Society of Automotive Engineers. This is a large and important and politically powerful institution in America. If the SAE embraced the metric system then we would use the metric system. So far the reverse has been true.

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anonymous
Anonymous 03/10/2012 20:41 PM

Only because Detroit rather selfishly didn't want the one-time conversion expense.

America was ready to go metric in the 80s.

Metric is superior to English in every way.

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anonymous
Anonymous 01/03/2012 15:35 PM

UGH!!!

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anonymous
Don Fallick 09/19/2011 00:56 AM

Another cool conversion math trick I discovered: to convert Celsius degrees to Farenheit, just multiply by two and add 30. You'll be within a couple of degrees at any temperature you're likely to experience. To go the other way (F to C), just subtract 30 and divide by two. WAY easier than multiplying by 9/5 (or is that 5/9? and adding/subtracting 32.

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anonymous
Anonymous 01/07/2012 12:13 PM

9C = 5F - 160

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anonymous
Enter your name 01/03/2012 14:08 PM

That doesn't really work. Sure you get close with 0 degrees C, but that is about it.
In fact, at one point, F and C are the same temperature. It is around -40 or something like that.

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anonymous
Anonymous 01/30/2012 00:50 AM

Yeah, I always love it when americans ask how cold it is in the winter here in northern Sweden, and I can tell them without having to convert.

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anonymous
Enter your name 09/17/2011 00:53 AM

or you could just give up the ridiculous Imperial system and use metric! Like the rest of the world. I mean really... this whole debate is ... stupid.

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anonymous
jeremybrett 09/16/2011 15:50 PM

i think the 'divide by 5, multiply by 8' trick is far easier than memorizing the fibonacci sequence, tho i suppose the above method is probably quicker for small enough numbers or for somebody who already has the sequence memorized

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anonymous
MathTeacher 09/16/2011 12:44 PM

The relationship isn't exactly coincidental. 1 km = 0.625 miles. As the fibbonacci sequence gets further out, the ratio of two terms in a row is 0.618. That's why you'll get an approximate answer. That is, f(n) / f(n+1) = 0.618, where f(n) represents the nth fibbonacci number.

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anonymous
pigbat 09/15/2011 10:35 AM

Another example of how math is just a made up science that conveniently works out.

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anonymous
Enter your name 09/13/2011 09:42 AM

mathematics is such a beautiful simple subject, but mathematicians make it so complex. It is no wonder they are confined to back rooms trying to crunch numbers for most of their working lives. Vailentz has pretty much got it right - 'convert kilometers to miles by multiplying by 6 and moving the decimal to the left one. To convert kilometers to miles you divide by 6 and move the decimal to the right one'. The decimal point is irrelevant if doing a quick kilometre/mph conversion - i.e. 80 kph x 6.... More

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anonymous
Anonymous 03/15/2012 07:06 AM

Real mathematicians don't crunch numbers. Really. If someone tells you they crunch numbers for a living they're most likely either a bad mathematician or an accountant.

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anonymous
Chris Dion 09/09/2011 21:59 PM

I have my own little trick I've used. Take a number like 50. Take half of 50 and add it. 50+25=75. Knock a digit off the original number, 50 becomes 5. Add that, 75+5=80. 50 miles = 80kms.

70miles=70+35+7=112kms

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anonymous
Rex Remes 03/24/2012 00:15 AM

That's just a 'tricky' way of multiplying by 1.6.

Add half is multiply by 1.5
That second step is adding 10% of the original number
Total result ... 1.6

Much easier to just remember 1.6

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anonymous
Anonymous 03/07/2012 17:05 PM

This makes so much more sense that the other big long explanation.

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anonymous
Anonymous 12/29/2011 21:44 PM

splendid understanding

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anonymous
werrtr 09/09/2011 21:31 PM

Why doesn't America convert to the metric system?Great Britain did it after they joined the EU.

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anonymous
Anonymous 09/11/2011 19:04 PM

The UK may have officially adopted metric measurements, but there are several exceptions - speed limit signs are still in miles per hour, and draught beer is still sold in pints.

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anonymous
Anonymous 09/12/2011 23:10 PM

Can I have a half-liter of beer please?...It just doesn't feel right....

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anonymous
Anonymous 09/17/2011 05:18 AM

that's why you go ahead and order a whole liter of beer.

can i have a liter of beer please?
now that sounds just fine to me

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anonymous
Anonymous 09/13/2011 11:51 AM

We use pint in Canada. It's now used more of a term or slang for a glass of beer than an exact measurement.

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anonymous
jdx 05/02/2012 11:56 AM

At a minor league baseball game in Texas one of the vendors sold draught beer in 12oz and 16oz. I asked for a pint. The guy said, "sorry, we don't sell pints, only cups"

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anonymous
Anonymous 04/12/2012 00:35 AM

Or sleeves if you feel like drinking twice as many twice as cold.

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anonymous
Anonymous 09/10/2011 14:28 PM

Because they don't have any reason to.

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anonymous
Vailentz 09/08/2011 11:33 AM

When I got stationed in Germany they taught us to convert kilometers to miles by multiplying by 6 and moving the decimal to the left one. To convert kilometers to miles you divide by 6 and move the decimal to the right one. It's quick and easy.

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anonymous
Mathguy 09/07/2011 16:16 PM

So let me get this straight... to get an **approximate** conversion from miles to kilometers, all I need to do is mentally multiply by a value equal to (1 + SQRT(5))/2???? How convenient!!!!

Isn't it easier to just divide the miles by the sine of a 38.42 degree angle?

Well, I guess it **is** more accurate than multiplying by pi over 2...

The relationship between the golden ratio and the ratio between kilometers and miles is inexact and totally coincidental. There is.... More

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anonymous
Bob 09/07/2011 10:23 AM

I just push the button on my dash and the magic numbers change.

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anonymous
John M. in AZ 03/17/2012 02:07 AM

That's what I do whenever I drive to Canada. No mental math involved . . . just enjoy the great scenery along the way.

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anonymous
Mac 01/05/2012 11:46 AM

I just know that 100mph is 100mph and 45km is 45km. Why convert, learn both.

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anonymous
Mac 01/05/2012 11:46 AM

I just know that 100mph is 100mph and 45km is 45km. Why convert, learn both.

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anonymous
Emma Williams 09/06/2011 06:20 AM

Just make sure you rent an amer. car, set your trip mileage to zero & when you arrive you will have the exact mileage. All you will have to do is enjopy your trip.

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