

Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa - pkrumins
http://www.catonmat.net/blog/using-fibonacci-numbers-to-convert-from-miles-to-kilometers/

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patio11
Relatedly, if you ever forget Avagadro's number, you can approximate it by
figuring out how many unique 5x5 bingo cards you can make by 24 words and a
free space. This will get you to within about 3% of the right number.

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tome
Intriguing. For those that were wondering, patio11 is talking about 24
factorial (or "24!").

Edit: corrected the post from 25 to 24. I got bitten by an off-by-one error in
Python's range!

~~~
patio11
Traditionally, the free space is stuck in the center of the card, and thus it
can be ignored for the purposes of the problem. The right answer is 24!

Incidentally, if you're trying to explain the results of this calculation to a
middle school English teacher, I recommend "More than there are grains of sand
on a beach." It relaxes the worry they really have and is non-specific enough
to avoid sounding threatening. (Ask me no questions I'll tell you no lies.)

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zck
The "Here's why this works" part was the best part of the article. Thanks for
writing more than "hey, look at this trick!"

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brown9-2
Can anyone who knows history comment on whether or not it is truly a
coincidence that the ratio of 1 mile to 1 kilometer approximates the Golden
Ratio?

As an aside, Wikipedia doesn't have much on the historical development of the
definition of a mile, but it has this amazing tidbit on the meter that I found
fascinating:

 _Historically, the metre ... was designed to represent one ten-millionth of
the distance from the Equator to the North Pole along Paris Meridian...._
<http://en.wikipedia.org/wiki/Metre>

~~~
Periodic
SI units:

Seconds came first. Since ancient times (Egypt or Babylon) people divided the
day into 24 parts and then sub-divided by 60 and by 60 again. This unit is
defined in relation to the rotation of the earth (which was later found to be
slowing, so it got redefined).

With seconds established, someone realized that a pendulum has the same period
regardless of the weight attached. The meter was defined to be the length of a
pendulum with a period of two seconds, or a half-period of one second.

Unrelated, but grams were defined to be the weight of one cubic centimeter of
water at (I believe) freezing/melting temperature.

Imperial units:

Well, these come from all sorts of places. Miles comes from paces, which are
related to the height of a man.

Conclusion:

SI units are derived from Earth's rotation and gravity, imperial units are
derived from functional and human characteristics. Unless you believe that the
proportions of the human body are related to other things in the cosmos
directly (DaVinci tried to show this) then it's just a coincidence.

~~~
eordano
I had forgotten about these relationships...

You are right, one gram is the weight of one cubic centimeter of water at 4ºC
(a little away from 0ºC so you don´t solidify by mistake).

I heard that imperial units used to change a lot, that the patron was the
current king at the throne. Do you know if this is true?

~~~
Xichekolas
4C is the temperature at which H20 is most dense, so it makes sense use that
temp when defining a mass in terms of a volume.

[http://en.wikipedia.org/wiki/Properties_of_water#Density_of_...](http://en.wikipedia.org/wiki/Properties_of_water#Density_of_water_and_ice)

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petercooper
You can use the same system to convert between British Pounds and US Dollars
right now too.. :-) It's been hovering around 1.6-1.62 for a while.

~~~
Keyframe
I wonder how many FX players are here in the HN community?

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jrockway
A few.

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mhartl
My favorite coincidence in this vein involves feet, nanoseconds, and the speed
of light. In special relativity, physicists typically work in "geometric
units", where _c_ = 1. Measuring length in feet and time in nanoseconds yields

    
    
      c = 0.983571056 feet/nanosecond
    

This is close enough to 1 for most practical purposes.

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jemfinch
Because multiplying/dividing by 1.6 is too hard?

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Xichekolas
The point is not that it is practical. The point is that it is interesting
(even if only by coincidence).

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kscaldef
Well, it is interesting, and occasionally practical for small numbers where
you might have the Fibonacci sequence memorized. But, I also found it rather
odd that the article seems to seriously suggest the technique of finding sums
of Fibonacci numbers to total arbitrary numbers you want to convert. People
who have difficulty multiplying 100*1.6 probably don't have the Fibonacci
sequence readily at their fingertips either.

~~~
ramchip
You forget Haskell programmers :)

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niyazpk
For me it is easier to multiply a number by 1.6 than to find the combination
of Fibonacci numbers forming the original number, finding the next Fibonacci
number for each of those and then adding the numbers.

Good trick though.

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kurtosis
My personal favorite is that there are approximately pi * 10^7 seconds in one
year.

~~~
blahedo
"How many seconds are there in a year? If I tell you there are 3.155 x 10^7,
you won't even try to remember it. On the other hand, who could forget that,
to within half a percent, pi seconds is a nanocentury." --Tom Duff, Bell Labs

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Luc
One of the estimating tricks I use the most is the Rule of 72 (
<http://en.wikipedia.org/wiki/Rule_of_72> ), which tells you how long it takes
for a number to double (or halve) given a yearly interest percentage (or
inflation). Just divide 72 by the interest rate and you get the number of
years it takes for your money to double. E.g. at a 3.6% interest rate (above
inflation!) it would take about 20 years for your investment to double.

~~~
roundsquare
Yeah, this is a nice trick. Also, 72 is a good number because it can easily be
divided by a bunch of numbers (1, 2, 3, 4, 6, 8, 9). 5 and 10 aren't hard
either, and these interest rates are the ones you are most likely to see.

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byrneseyeview
This is basically <http://xkcd.com/687/> with twice the setup and none of the
punchlines.

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teeja
Kilometers to miles: multiply by 2*pi, move decimal left one place. About 1%
error.

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vgurgov
very useful, thanks :) "Coincidentally, there are 1.609 kilometers in a mile,
which is within 0.5% of the Golden ratio." was the only interesting sentence
for me

~~~
kscaldef
I don't know why you're being downvoted for this statement. It's true, the
entirety of the "why" is in that sentence, which you'd think would be what
this community was interested in.

