![]() ![]() In the spirit of Pumpkin Spice/Halloween season (pick your favorite), I thought this one would be appropriate to include.Ī pumpkin is generally roundish in shape, but, for the sake of this joke, we’re going to assume it’s perfectly spherical. What do you get if you divide the circumference of a jack-o-lantern by its diameter?… A Pumpkin Pi!.Which means that we transform “shit” from imaginary to real. So, by taking, we just get the quantity “shit.” Furthermore, a square power is undone by a square root, thereby maintaining the quantity inside and simply changing its power. Like I said earlier, all squared numbers are positive so, when we square a negative number, we can proceed. When a negative number is put under an even root (square root, fourth root, etc.), the result is imaginary, and we have to deal with i, which isn’t always as fun as it may sound (even though I’m sure you find that positively riveting).īuuuuut the problem disappears when we raise the imaginary quantity to an even power. Well, not really (but if you talk to some quirkier mathematicians, they’ll certainly act like that’s the case).Īlthough most numbers we’re aware of are called “real numbers,” there are actually these things called “ imaginary numbers.” These are numbers that can’t exist, but that we can theoretically imagine. Think about it like this: every time you square a number, regardless of its sign, it becomes positive… So what happens when we try to take the square root of a negative number? If you thought numbers were all tangible – they may be confusing, but hey, at least they exist – then I’m sorry to tell you, but you are sorely mistaken. Maybe it’s a Good Will Hunting kind of thing, except without the janitor. So basically, even though the guys ordering beer were all mathematicians, they sucked at calculus compared to the bartender. I won’t bore you with another equation, or by actually taking the limit, but, by doing a few very simple calculations, we can see that, although the mathematicians will get infinitely close to a second beer, they will never actually reach two servings – regardless of how many orders they make. Now, even though we know how much each individual mathematician will drink, we don’t know how much beer infinitely many mathematicians will drink. If we label the first mathematician (the one who, like an actual human being, orders a whole beer instead of a fractional one) as n=1, and each successive mathematician as n=2, n=3, etc., we generate this equation for the amount of beer each mathematician will order: In the joke (it made me laugh, so I’m going to stick with it being a joke), each mathematician orders a smaller fraction of the drink than his predecessor. This is a classic example of an asymptote, a value which will be steadily approached, but never physically reached. The first orders a beer, the second orders half a beer, the third orders a quarter of a beer, and so on… After the seventh order, the bartender pours two beers and says, “you’re all idiots.” An infinite number of mathematicians walk into a bar.
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