Follow Slashdot blog updates by subscribing to our blog RSS feed


Forgot your password?
Check out the new SourceForge HTML5 internet speed test! No Flash necessary and runs on all devices. ×
Math Idle

Mathematicians Use Mossberg 500 Pump-Action Shotgun To Calculate Pi 311

KentuckyFC (1144503) writes "Imagine the following scenario. The end of civilization has occurred, zombies have taken over the Earth and all access to modern technology has ended. The few survivors suddenly need to know the value of pi and, being a mathematician, they turn to you. What do you do? According to a couple of Canadian mathematicians, the answer is to repeatedly fire a Mossberg 500 pump action shotgun at a square aluminum target about 20 meters away. Then imagine that the square is inscribed with an arc drawn between opposite corners that maps out a quarter circle. If the sides of the square are equal to 1, then the area of the quarter circle is pi/4. Next, count the number of pellet holes that fall inside the area of the quarter circle as well as the total number of holes. The ratio between these is an estimate of the ratio between the area of the quarter circle and the area of a square, or in other words pi/4. So multiplying this number by 4 will give you an estimate of pi. That's a process known as a Monte Carlo approximation and it is complicated by factors such as the distribution of the pellets not being random. But the mathematicians show how to handle these too. The result? According to this method, pi is 3.13, which is just 0.33 per cent off the true value. Handy if you find yourself in a post-apocalyptic world."
This discussion has been archived. No new comments can be posted.

Mathematicians Use Mossberg 500 Pump-Action Shotgun To Calculate Pi

Comments Filter:
  • by Anonymous Coward

    Trace a circle on the ground and drop stones at it.

  • That's better than the part of pi I have memorized, 3.1415926. I had no idea I could waste valuable shotgun shells calculating pi to such precision.
  • by Anonymous Coward on Monday April 14, 2014 @08:39AM (#46746579)

    In a post apocalypse zombie filled world I'd just say "3" and keep the shotgun shells.

    • by plover ( 150551 ) on Monday April 14, 2014 @09:07AM (#46746927) Homepage Journal

      How about killing two birds with one stone? Stand the zombies in a circle, and fire the rounds at them. Count the number of dead zombies. Now you've got an approximation for Pi AND a bunch of dead zombies. Win-win.

      • AND a bunch of dead zombies.

        What's a dead zombie? Is this some kind of recursion?

        (Getting old has a lot of advantages, but one of the disadvantages is that it's harder to keep track of popular memes. I mean, I never understood the whole "vampire" thing, and now we're on to zombies. What's next?)

  • um.... (Score:5, Insightful)

    by johnholstein ( 1735990 ) on Monday April 14, 2014 @08:40AM (#46746583)
    ":...being a mathematician, they turn to you." You're not much of a mathematician if you don't already know the value of Pi out to several decimal places without the need to expel valuable ammo in an experiment. /john
    • What's more, if you are able to remember the details of the experiment, you are more than capable of remembering a few decimals of what is probably the most widely known constant in mathematics.

    • ":...being a mathematician, they turn to you." You're not much of a mathematician if you don't already know the value of Pi out to several decimal places without the need to expel valuable ammo in an experiment. /john

      Yeah, and how hard is it to divide 22 by 7 with a twig in the dirt, "Mr. Mathematician"? That's also an acceptable approximation of Pi that is 4.0249943477E-2 percent off the "true value". I think the colder climate and/or recreational hallucinogens has slowed those Canadians' brains a might. Maybe that's the way to avoid zombies, after all.

    • Relevant SMBC [].

    • It's just a way for mathematicians to get people to stop asking inane questions during the apocalypse.

      "Can you estimate Pi?"
      "Sure. Hand me that shotgun."

      "Do you know Euler's Number offhand?"
      "Of course. Hand me that bazooka."

      "What's Pythagoras' constant?"
      "Seriously? Do you see a tank around here?" Eventually you get left in peace.
  • Only in America... (Score:5, Insightful)

    by Max_W ( 812974 ) on Monday April 14, 2014 @08:40AM (#46746587)
    a gun to calculate Pi value...
    • by Nidi62 ( 1525137 ) on Monday April 14, 2014 @08:44AM (#46746641)

      a gun to calculate Pi value...

      According to a couple of Canadian mathematicians,

      I didn't realize we had annexed Canada recently. I hope we didn't also get Quebec.

      • Re: (Score:2, Troll)

        by ArcadeMan ( 2766669 )

        With the Conservatives acting like dictators and making bullshit pro-corporations, anti-people laws, I hope Québec splits soon enough.

        Then it will pave the way for the USA to let Texas and California go their own separate way, too.

      • I hate to break it to you, but the ancient term "America" refers to the whole continent, Canada included.

    • by cold fjord ( 826450 ) on Monday April 14, 2014 @08:45AM (#46746661)

      Don't be silly, the method should work in any country.

    • a gun to calculate Pi value...

      Not only are they Canadian, they're French Canadian. Calling them American is worse than calling them Canadian as the Québecers would rather be their own country all together. I just think they're smoking something to not use simple long division to calculate Pi, especially as a university research mathematician. I mean, really! 22 / 7 = closer to Pi than their stupid shotgun embarrassment.

  • Ask an old person? (Score:5, Insightful)

    by gb7djk ( 857694 ) * on Monday April 14, 2014 @08:41AM (#46746593) Homepage
    The engineers answer: ask someone who went to school before the zombies arrived. Mind you, an engineer probably wouldn't have to bother. Rhetorical question: I wonder how Euclid managed?
    • by Roxoff ( 539071 ) on Monday April 14, 2014 @08:50AM (#46746703) Homepage

      Euclid's Shotgun? Is that much like Occam's Razor, or Shrodinger's Cat?

    • I thought the engineer's answer was, "More than three and probably less than twenty."

      Oh, no, wait, that's the answer to "What's 2+2?"

    • by Kjella ( 173770 )

      Rhetorical question: I wonder how Euclid managed?

      I know what rhetorical means but really, there's so many obvious ways. Take a piece of string, tie down one end and draw a circle in the sand with the other. Now use the same piece of string to measure out the circle. You'll get an approximation of pi more than good enough for any practical purpose, the only thing "special" about it is that numbers that aren't fractions like pi, e and the square root of 2 was fucking with their understanding of math. Even the ancient druids of Stonehenge could map out a cir

    • Rhetorical question: I wonder how Euclid managed?

      Slingshot. It is a slower process but still provides a useful answer when under primitive conditions.

  • Number Theory With A Machinegun - The Problem Solving Powers Of The M2 Browning .50 Caliber Heavy Machinegun :)

    • by i.r.id10t ( 595143 ) on Monday April 14, 2014 @08:43AM (#46746629)

      Indeed, if a Ma Deuce doesn't solve the problem either the problem is unsolvable or you just need more ammo.

    • by Xest ( 935314 )

      If you mount it on a sliding rail running parallel to and pointing at an infinite length horizontal board with an infinite belt of ammo and set it moving with a correctly calibrated exponentially increasing speed then you can use it to reproduce, using a measurement of the distance from the start, the Fibonacci sequence.

      Useful if you're in a zombie apocalypse and you need to remember it.

      Do I get my own Slashdot article now?

  • I would just approach my fellow humans with the Mossberg 500 and ask if anyone remembers the value of pi. I live in Silicon Valley: even the zombies would remember it.
    • And as a mathematician, I would already remember more significant figures for pi than I would likely be able to get from a bullet-scatter pattern.
  • what's next? researchers use beads to do arithmetic?

    • by mysidia ( 191772 )

      what's next? researchers use beads to do arithmetic?

      Next article is on how to use paper logarithm tables to perform calculations in a post-apocalyptic world.

  • Alright boys, we used up all our limited ammo but at least we know pi before we die!
  • Archimedes (Score:2, Insightful)

    by Anonymous Coward

    neither had nor needed a shotgun to calculate pi to 2 significant digits, which I'd wager is significantly closer than you're likely to get...

  • As a mathematician, the best part of it is probably asking your department to put the rifle on your research funds. I'm sorry, professor Dumoulin, you need *what*?
  • We have only been using shotguns for fractions.
  • by MrKaos ( 858439 ) on Monday April 14, 2014 @08:51AM (#46746707) Journal
    Do you put the zombies in front of the square alluminum plate?
  • by Anonymous Coward

    In a post-apocalyptic world, why not fix the mistake and calculate the correct constant, tau []?

  • Sounds like they undershot.

  • 3.14159265358... or something like that. That could be wrong. But my memory is usually worth "Good Enough" engineering.

    And I think it's a lot harder to remember ... What the hell do I do with this shotgun again?
  • by CQDX ( 2720013 ) on Monday April 14, 2014 @08:57AM (#46746785)
    First, pack at least couple solar powered calculators. You can get cheap scientific calculators at the dollar store. They'll be worth their weight in gold during the second Renaissance. Second, don't give the mathematician any weapons. Let him be a mule, carrying any tech books you find along the way. Give him a pencil and pad of paper and let him re-derive the whole of known mathematics.
    • First, pack at least couple solar powered calculators. You can get cheap scientific calculators at the dollar store.

      The dollar store? My Ti-34 (that I still use) cost $74 you insensitive clod! (And it has pi to 9 decimal places as a built-in constant.)

  • A real nerd would know how to calculate Pi from scratch, no shotgun required...

    Pi = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ... (keep going until you get the number of decimal places you need.)

    Why bother with the shotgun and waste the rounds conducting this worthless experiment. You are proving nothing but that you know how to draw a square and an arc and count.

    OR, just get some unsuspecting length of string, a ruler and a round object like a jar or large can. Measure the circ

    • A real nerd would know how to calculate Pi from scratch, no shotgun required...

      Pi = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ... (keep going until you get the number of decimal places you need.)

      Gaaaa! What? How about 22 / 7 . Way closer, less painful. Nerds do it more efficiently and more accurately. That was about as bad as the shotgun method, maybe worse. I stopped doing the math at (4/15) when the result was 3.01[something] and adding (4/17) was 3.25[something] ... Not even close.

    • by bmo ( 77928 )

      Why bother with the shotgun and waste the rounds conducting this worthless experiment.

      Because it's fun.

      You must be loads of laughs at a party.


  • by netsavior ( 627338 ) on Monday April 14, 2014 @09:00AM (#46746827)
    "And he made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26

    30/10 = 3

    Bible Pi = 95.493% accurate
    Shotgun Pi = 99.67% accurate
    • Research back in the 1930s discovered that there's more to that verse than appears. In Hebrew, the letters are also numbers, and the number values of letters and words are often very significant to the reading. There is a 'jot' ('jot' and 'tittle' are like diacritic marks) in the original, which here means, "look deeper". So with a bit of deeper analysis, one finds that the letters there turn out to make up a fraction. I forget what the fraction is, but it's something like 31/222 or some such, and with the fraction the value is within 1% or less of pi. This is discussed in one of Chuck Missler's research texts, about that book in the Bible.

      • by Anonymous Coward on Monday April 14, 2014 @09:35AM (#46747259)

        That's a lot of numerological bullshit. The truth is much simpler. The Bible says it's 10 cubits across and 30 cubits around. The diameter is provided with one significant figure, and the circumference is also provided with one significant figure. Dividing the two gives you pi... to one significant figure. Anyone who says "this proves that the Biblical authors thought pi = 3.00 [3 significant figures]" must not have done very well in physics class.

        • Re: (Score:2, Troll)

          Nope. You're just presenting a more subtle version of numerological bullshit.

          Having only one significant digit means that the actually value for 10 is somewhere between 6 and 14 and the value for 30 is somewhere between 26 and 34. Measurements were not that inaccurate (you don't really think they only have a 15 foot rope to measure with and absolutely nothing else, do you?).

          10 and 30 have 2 significant digits even if you assume that they rounded to whole numbers and didn't want to use fractions or decimal

  • Measure the diameter and circumference then divide with a slide rule. And get off my lawn.
  • Shotgun pattern distribution is governed by several factors, including shot quality / material, wad design, barrel design, hull design, forcing cone length / shape, but most especially choke. Steel shot will rip up some chokes. Chokes can creep (particularly on a hot Illinois day). Wadding can foul a barrel.

    I wonder if these were controlled for.

    • Glad I'm not the only one whose first question involved the choke.

      BTW, you forgot "windage" in your variable list.

      • I never noticed it, at least not in the ranges as described. Sometimes the clay can bounce a bit, but even that is rather marginal if you are shooting correctly.

        • Depends on the wind; we've been getting 30-40 Mph gusts the last few days, which could have some effect at 20 meters. 'Specially with grouse rounds.

          At least TFA mentions the load they used: "cartridges composed of 3 dram equivalent of powder and 32 grams of #8 lead pellets"

  • The above would only work if the spread were random. I would expect it to cluster with a greater density of pellets in the middle. Does anyone know how random the spread is?
  • Dumoulin and Thouin’s idea is to use the distribution of shotgun pellets rather than sand or rice (which would presumably be in short supply in the post-apocalyptic world).

    really...sand in short supply?

    and shotgun shells aren't?

  • Swap the gun for some tin snips and a scale. You could simply weigh the whole target, then snip out the quarter circle and weight that. Take the ratio of the weights, and you're done.

    Save the ammo for something else.

    • Swap the gun for some tin snips and a scale.

      Why not swap the gun for an encyclopedia instead? Come to think of it, use the gun to threaten the encyclopedia salesman. Win-win.

  • If you really want to use this method to calculate pi, here's how to actually go about it. What you need is a hundred yards or so of string, four stakes, a stick and something that's a reasonable approximation to a right-angle (perhaps a piece of a cardboard box salvaged from the apocalypse). If you're really stuck for a right angle you can construct one with three stakes and a piece of string by putting two stakes in the ground and using the string to mark a straight line between them, then tying one end

    • Couldn't you just draw out a circle with string and a stake, then lay a second piece of string over the drawn circle, then measure the two bits of string with a stick?

  • by BlackPignouf ( 1017012 ) on Monday April 14, 2014 @09:32AM (#46747221)

    Another method : []

  • Nothing special. (Score:4, Insightful)

    by 140Mandak262Jamuna ( 970587 ) on Monday April 14, 2014 @09:32AM (#46747223) Journal
    This was one for the first exercises done in Introduction to Computing 201, using a random number generator to find the value of PI. I did it in FORTRAN back in the days with punch cards in IBM370/155. Recently I did it again to teach myself MPI. This is a basic exercise in Probability and Statistics course. Once can draw a circle in fly paper. The number of bugs caught inside the circle to total number of bugs caught would be approximately PI/4. But that would get you a better headline, "Bugs commit suicide to tell us the value of PI".
  • Doesn't this rely on some rather shaky assumptions, mainly that the spread of the shotgun pellets across the target is completely random (which we know it isn't; the likelihood of a pellet hitting diminishes as you move away from the centre)?
  • ... that the Ancient Greeks managed to do better at calculating Pi, all without shotguns!
  • ...they could take the same sheet of aluminum, weigh it, cut along the arc that they already inscribed and weigh the quarter circle, and multiply the ratio in the weight by four. Or, they could take a length of string, carefully line it up with the arc they already inscribed and snip it, form the ratio of its length $\pi R/2$ and the length of a side of the square R, and multiply by 2. Or they could evaluate using any one of a number of summed series. Or any of a number of other measurement-based geometr

  • Apocalypse, eh?

    I would probably be using the mathematician standing in the corner wasting shotgun shells calculating Pi as bait during the next zombie attack.

    Just sayin.

  • Unless solar powered calculators magically disappear
    and people forget about how to use string and rulers.

  • by Deadstick ( 535032 ) on Monday April 14, 2014 @10:13AM (#46747651)

    Just calculate 4-4/3+4/5-4/7+4/9-4/11... to as many significant figures as you'd like. It converges to exactly pi.

  • by Trailer Trash ( 60756 ) on Monday April 14, 2014 @10:18AM (#46747707) Homepage

    Come to Tennessee or Indiana and drive out in the country. Pretty much half the stop signs have already been prepped for you - you just have to count holes.

  • by RevWaldo ( 1186281 ) on Monday April 14, 2014 @11:59AM (#46748757)
    There are definitely old school reference books with the value of pi to hundreds if not thousands of decimal places.

    Unless the zombies take up reading or eat books, and you don't break your glasses, we're good to go.


Truly simple systems... require infinite testing. -- Norman Augustine