6 ms·
Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa
- zck 17y agoThe "Here's why this works" part was the best part of the article. Thanks for writing more than "hey, look at this trick!"
- patio11 17y agoRelatedly, 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.
- tome 17y agoIntriguing. 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!
- jonp 17y agoHe's actually talking about 24! not 25!. (Maybe because the free square is in a fixed position?) 24! = 6.20e23; and Avogadro = 6.02e23.
- patio11 17y agoTraditionally, 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.)
- WilliamLP 17y agoI sometimes enter a bingo hall with exactly 12 grams of carbon-12, and then I fill out a card for every atom, knowing that I'll have covered all combinations when I run out.
- deleted 17y ago[deleted]
- pkrumins 17y agoThe original question was how to convert 19 miles to km. First decompose it into a sum of Fibonacci numbers: 19 = 13 + 5 + 1 Then find the next Fibonacci number for each one of them: 13 -> 21 5 -> 8 1 -> 2 Then sum them up to get the result in kilometers: 21 + 8 + 2 = 31km Which is within 1.36% of the correct answer (the correct answer is 30.57km.)
- dazmax 17y agoOr you could do 21 - 2 -> 34 - 3
- jonp 17y agoI thought the OP was alluding to the slight ambiguity because 1 appears twice in the Fibonacci sequence. You could interpret the approach two ways and do either 21 + 8 + 2 = 31 km or 21 + 8 + 1 = 30 km. Happily these span the correct answer of 30.55km.
- gjm11 17y agoIn this situation I tend to pretend that 1 -> 1.5. (Or, indeed, 1.6, but generally that looks like claiming more accuracy than is really justified.)
- kscaldef 17y agoOkay, but you could also say 19 = 20 - 1 then multiply by 1.6 20 -> 32 1 -> 1.6 and get the estimate 19mi = 30.4km, which is even closer and seems rather easier to me than figuring out a set of Fibonacci numbers which sum to 19.
- dutchflyboy 17y agoWell, if you had actually read the article before asking, you would have known the answer. (you change the number into the sum of several fibonacci numbers, convert each one, then sum the result again).
- vgurgov 17y agovery 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 17y agoI 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.
- byrneseyeview 17y agoThis is basically http://xkcd.com/687/ http://xkcd.com/687/ with twice the setup and none of the punchlines.
- niyazpk 17y agoFor 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.
- brown9-2 17y agoCan 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 http://en.wikipedia.org/wiki/Metre
- pkrumins 17y agoYes, I'd like to know as well. I was unable to find any references so far. I am truly interested.
- lmkg 17y ago"Mile" also means a thousand, coincidentally. In ancient Rome, it was the distance of one thousand paces. Note that a "pace" was two steps, i.e. one stride with each leg.
- cruise02 17y agoSeems like it's just a coincidence. According to The Straight Dope (http://www.straightdope.com/columns/read/637/whats-the-origin-of-miles-and-yards http://www.straightdope.com/columns/read/637/whats-the-origi...) the length of a mile is based on the length of a Roman pace (or stride).
- Timothee 17y agoI remember that definition from high school. It's funny how useless that definition is, in that, knowing it doesn't help you figure out what it really is. The newer definition: "In 1983, the metre was redefined as the distance travelled by light in free space in 1⁄299,792,458 of a second." always kind of bothered me because it sounds like it went like this: "Ok, so we defined the speed of light as 299,792,458m/s and it's all over textbooks and formulas, but the thing is that our current definition of a meter sounds a little bit like a guess. So let's just reverse the speed of light and we're good!" It feels like a backronym to me (http://en.wikipedia.org/wiki/Backronym http://en.wikipedia.org/wiki/Backronym)
- petercooper 17y agoYou 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.
- pavel_lishin 17y agoI propose that we change the Golden Ratio to reflect the current exchange rate, daily.
- saurabh 17y agoGolden.
- Keyframe 17y agoI wonder how many FX players are here in the HN community?
- jrockway 17y agoA few.
- jemfinch 17y agoBecause multiplying/dividing by 1.6 is too hard?
- Xichekolas 17y agoThe point is not that it is practical. The point is that it is interesting (even if only by coincidence).
- kscaldef 17y agoWell, 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 17y agoYou forget Haskell programmers :)
- kurtosis 17y agoMy personal favorite is that there are approximately pi * 10^7 seconds in one year.
- Periodic 17y agoNice. And only 0.5% off.
- amalcon 17y agoHah! It takes the Earth about five million seconds to travel through one radian of its orbit. That... seems more useful to know than it actually is.
- blahedo 17y ago"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
- ssp 17y ago"pi seconds in a nano-century" is how I remember it.
- Luc 17y agoOne of the estimating tricks I use the most is the Rule of 72 ( http://en.wikipedia.org/wiki/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 17y agoYeah, 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.
- mhartl 17y agoMy 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.
- teeja 17y agoKilometers to miles: multiply by 2*pi, move decimal left one place. About 1% error.