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

Posted
by
samzenpus

from the less-common-core-math dept.

from the less-common-core-math dept.

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."*
## Drop stones in a circle (Score:2, Insightful)

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

## So handy (Score:2)

## Keep the shells (Score:5, Funny)

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

## Re:Keep the shells (Score:4, Funny)

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.

## a bunch of dead zombies (Score:3)

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?)

## Re: (Score:2)

## Re: (Score:2)

For garter accuracy...

Why not use an elastic garter?

## Re: (Score:2)

Or use the shotgun itself to sweep out a circle of diameter "1 shotgun" and place shells around the perimeter thus estimating the circumference as "x shells". You can then use the shells to measure the length of the shotgun to get a conversion ration between the two units. For garter accuracy you can use a longer gun and or smaller ammunition, and/or use the gun to sweep out a radius instead of the diameter.

One advantage to using the US system of measures is you get comfortable with units based around the "whatever some dude had in his pockets at the time" standard and converting between arbitrary systems for measuring the same thing.

yes, very accurate. my challenge is I know some conversions by heart, but only a couple. for example, 453 g/lb. so to go from short tons to metric tons i have to go ton->lb->g->kg->mt

## um.... (Score:5, Insightful)

## Re: (Score:2)

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.

## Re: (Score:2)

":...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.

## Re: (Score:3)

Relevant SMBC [smbc-comics.com].

## Re: (Score:3)

"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)

## Re:Only in America... (Score:4, Funny)

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)

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.

## Re: (Score:2)

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

## Re: (Score:3, Interesting)

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

Nope - that would be "North America."

Hey, if you're going to be a pedant...

Ok, since we're being pedantic: technically, "America" refers to the entire landmass (made up of the continents of North and South America and associated islands). Still includes Canada, though.

## Re: (Score:2)

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

Nope - that would be "North America."

Hey, if you're going to be a pedant...

Ok, since we're being pedantic: technically, "America" refers to the entire landmass (made up of the continents of North and South America and associated islands). Still includes Canada, though.

I've never heard anyone refer to the American Continents as a singular; it's always been "the Americas."

Aw, geez, did I really get drawn back into this? You sneaky bastards.

## Re: (Score:2)

Nope - that would be "North America."

Hey, if you're going to be a pedant...

Ok, since we're being pedantic: technically, "America" refers to the entire landmass (made up of the continents of North and South America and associated islands). Still includes Canada, though.

I've never heard anyone refer to the American Continents as a singular; it's always been "the Americas."

Aw, geez, did I really get drawn back into this? You sneaky bastards.

I've always interpreted America to refer to the major continental land mass of North and South America and Americas to include all of the islands.

## Re:Only in America... (Score:5, Funny)

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

## Re: (Score:2)

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.

## Re: (Score:2)

Last time I checked, actually, it is. It's just not in the USA.

## Re: (Score:2)

So, Americans fail at maths and geography.

I'd feel smugly self-satisfied about that if it weren't for the fact that they clearly win in the impending zombie apocalypse.

## Re: (Score:2)

I have never heard anybody refer to north america as "america". I have heard "americas" to be north and south america.

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

## Re:Ask an old person? (Score:4, Funny)

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

## Re: (Score:2)

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?"

## Re: (Score:3)

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

## Re: (Score:2)

The babylonians [exploratorium.edu] and God's favourite people [st-and.ac.uk] thought that pi=3. Hey, it's good enough for government work, and probably for fighting zombies.

## Re: (Score:2)

Rhetorical question: I wonder how Euclid managed?

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

## I think I just found a title for my thesis (Score:2)

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

## Re:I think I just found a title for my thesis (Score:4, Funny)

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

## Re: (Score:2)

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?

## easier way (Score:2)

## Re: (Score:2)

## A really slow news day (Score:2)

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

## Re: (Score:2)

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.

## Sweet (Score:2)

## Archimedes (Score:2, Insightful)

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...

## Funding (Score:2)

I'm sorry, professor Dumoulin, you need*what*?## Huh. Who knew... (Score:2)

## I don't understand (Score:4, Funny)

## Why calculate pi? (Score:2)

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

## Sounds like... (Score:2)

Sounds like they undershot.

## You're writing this to geeks you know.... (Score:2)

And I think it's a lot harder to remember

## 2 tips for preppers (Score:5, Insightful)

## Re: (Score:2)

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.)

## What would a real nerd do? (Score:2)

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

## Re: (Score:2)

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.

## Re: (Score:2)

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.

--

BMO

## So wait, shotguns are more accurate than the bible (Score:5, Interesting)

30/10 = 3

Bible Pi = 95.493% accurate

Shotgun Pi = 99.67% accurate

## Re:So wait, shotguns are more accurate than the bi (Score:4, Interesting)

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.

## Re:So wait, shotguns are more accurate than the bi (Score:5, Insightful)

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

## use a piece of string (Score:2)

## Chokes (Score:2)

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.

## Re: (Score:2)

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

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

## Re: (Score:2)

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.

## Re: (Score:2)

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"

## Anyone know random the spread of the Mossberg is (Score:2)

## those damn sand-eating zombies! (Score:2)

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?

## Just weigh the aluminium target (Score:2)

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.

## Re: (Score:2)

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.

## Hmmm (Score:2)

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

## Re: (Score:2)

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?

## Buffon's needle (Score:3)

Another method :

http://en.wikipedia.org/wiki/B... [wikipedia.org]

## Nothing special. (Score:4, Insightful)

## Assumptions? (Score:2)

knowit isn't; the likelihood of a pellet hitting diminishes as you move away from the centre)?## Or just drop some matchsticks (Score:2)

http://en.wikipedia.org/wiki/B... [wikipedia.org]

## Amazing to think ... (Score:2)

## Or... (Score:2)

...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

## Why mathemeticians won't survive. (Score:2)

Apocalypse, eh?

I would probably be using the mathematician standing in the corner wasting shotgun shells calculating Pi as

baitduring the next zombie attack.Just sayin.

## Unlike computing, math tech will still work (Score:2)

Unless solar powered calculators magically disappear

and people forget about how to use string and rulers.

## Infinite series (Score:3)

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.

## Time saving tip for these guys (Score:5, Funny)

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.

## Or find a library? (Score:3)

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

.

## Re: (Score:2)

This just screams of mathematicians pretending to be engineers.

## Re: (Score:2)

Nonaya eggheads is gonna last through the zombies, man.

I think the article is firmly tongue in cheek. There is no practical use here, but it is a fun way to teach some fundamentals of geometry and statistics.

## Re:Um, no? (Score:5, Interesting)

I responded with something along the lines of, "I'm sure they figured out that mowing in circles is theoretically more efficient, except that most lawn mowers have a finite turn radius that makes it impractical and push mowers can't cut while turning since they have to be lifted."

"Also, people tend to get dizzy going in circles for more than a few seconds, so unless they employ a ballerina to do their lawn mowing, all they showed it why you don't ask a mathematician to solve an engineering problem."

## Re:Um, no? (Score:4, Insightful)

Im not clear how it could be "more efficient". Your average speed will be higher on the straight-aways, and no matter what shape you do you will have to mow the entire area of your lawn. How you fill it in doesnt change the amount needing to be done.

## Re: (Score:2)

## Re: (Score:3)

or maybe your wife is tired of you talking to her like she's a child.

## Re: (Score:2)

## Re: (Score:2)

Or maybe they're smarter than you think:

https://www.youtube.com/watch?... [youtube.com]

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:2)

## Re:Um, no? (Score:5, Funny)

And that is of course the reason these guys used this particular method to estimate pi: not "science", but as an excuse to blast away with a shotgun. As if you need an excuse for that...

## Re: (Score:2)

When we rebuild industrialized society, I'll invent a precise means of measuring (something like a ruler?), some kind of calculating device (something like an abacus), and end up with an approximation sufficient to exceed the abilities of my tools to measure. Now, about

fireandthe wheel...Yes, I know -somebody just wanted to talk about various interesting ways to approximate the value of pi. Ever consider dropp

## Re:Um, no? (Score:4, Insightful)

And you waste a load of shotgun shells that are going to be extremely valuable in the post apocalypse.

## Re: (Score:2)

## Re: (Score:2)

I feel like this should be the gold standard. Whatever method you use, it should be either a lot cheaper or a lot more acurate; if neither, you chose very poorly.

## Re:fixing the parent posting (Score:5, Interesting)

I'm wondering if they got results without a choke, or at full choke. This might be statistically significant.

## Re:fixing the parent posting (Score:5, Funny)

## Re:fixing the parent posting (Score:5, Funny)

They would only need confidence in the random distribution of holes in the target.

Goddamn mathematician wasting precious ammunition to have a statistics wank-fest after MY goddamn zombie apocalypse?

I'd put a random distribution of holes in his worthless head!

## Re: (Score:3)

I'd put a random distribution of holes in his worthless head!

I believe you mean psuedorandom. (*bang*)

## Re: (Score:3)

You are the best kind of correct.

Technically correct.

## Re: (Score:2)

## Re: (Score:3)