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Math for fun and glory
Anti-Pi Rant, 3/14/14
Sorry, Pi lovers! Maybe pick a better favorite number next time? Created by Vi Hart.
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At2:40she said: "If you threw a dart and picked a random number of the number line, the chance of getting a rational number is exactly 0"
My question is simple; Why?(71 votes)
If you have a set of anything.... say a deck of 52 cards, the odds of picking any one card form that deck is 1 in 52. If the deck has infinite cards, then the odds of picking that same card is then 1 out of infinity. 1 divided by infinity is zero. That is what she means. Picking any non-rational number out of a set of infinity can be any finite large number divided by infinity. BIG INSANE EPICALLY LARGE NUMBER divided by infinity is still .... zero. So she's right!(9 votes)
- pi can be written, when in fraction form, as 22/7, so doesn't that technically make it rational? Or is this fraction just an approximation of the real value of pi?(2 votes)
It is an approximation. It is one of the more famous ones because when Archimedes calculated pi, he put inner and outer bounds on a circle with polygons, and that was one of his less accurate approximations. It is greater than pi because it is approximately equal to: 3.14285714286. A better approximation would be 355/113 which is good to 6 decimal places. The only ones better than that have denominators greater than 30,000.(6 votes)
- why do we HAVE pi day. i mean pi is cool (like tau), but why do we have a holiday for it?(8 votes)
Why do we have the Grand Holiday of Pi Day? Good question. As Vi says in "Pi is (still) wrong," the reason schools teach you all the equations with Pi instead of Tau and Christopher Columbus discovered America (which he didn't) and make Columbus Day a Grand Holiday -- the reason is because that's what people have been doing for a very long time, and people naturally don't like change. They like order and routine. If somebody started celebrating Pi Day, other people, not knowing about Tau, would say, "Pi Day? That sounds cool!" So now Pi Day is a Grand Holiday. If people all of a sudden started celebrating Tau Day, in fifty years it would be a Grand Holiday, too. So to answer your question, we Columbus Day and Pi Day and Washington's Birthday and Lincoln's Birthday and President's Day and Talk Like a Pirate Day is because that is what people have done for a very long time, and they don't want to change it. Speaking of which, you could make E Day into a Grand Holiday. E or Euler's Number is another irrational, approximately 2.718281828459 . . .
That might answer your question.
Godspeed!
--Blue Leaf(6 votes)
At 2 minutes and around 44 seconds, why is it you say that if you throw a dart on the number line there is a zero percent chance of getting a rational number? The definition of rational is if a number can be written as a fraction, or a decimal that terminates or repeats. There are gazillions of numbers that can be rational, and throwing a dart on a number line can bring you to one of those numbers. Another question. The whole point of the video was to understand that pi is not infinite, yet there are infinite numbers to pi as you claimed at 1 minute and around five seconds. If there are infinite NUMBERS, then why is pi not infinite?. Pi is a number after all.(4 votes)
There are an infinite number of rational numbers, but there are even more irrational numbers. We can actually count the number of rational numbers, but the number of irrational numbers are uncountable and so infinitely more common. As a result, the chance of choosing a rational number out of all real numbers is zero.
There are an infinite number of DIGITS to pi, but pi is still not infinite. Every number in existence has an infinite number of digits. Does that make every number in the world infinite? Either way, pi is nothing special to be venerated.(8 votes)
how can pi be not infinite?(4 votes)
Pi is a number that is three and a bit. That isn't very big. The digits of pi go on infinitely but that is not really pi itself, just a load of decimal digits that help to approximate it. Draw a line. Draw a semicircle on that line. That semicircle is pi relative to the radius you used, of course. That is more fundamentally pi than any sequence of digits. Doesn't look very infinite does it? You didn't even use up the whole pencil. ;-) So there are infinite things about pi, but no more so than any other irrational number or maybe even any other number. This stuff is not what makes pi special, That semicircle you drew (or imagined) is what makes pi special.(3 votes)
- I don't get how the chances of throwing a dart on a number line and getting a rational number is 0. There has to be some chance. For example, 5 is rational so there is a tiny chance that you will get a rational number.(3 votes)
Well, because the chance is infinitely small, it is equal to zero. See the Vi Hart video about this property if you don't believe that 0.000...001=0.(3 votes)
HA HA HA! Go to2:24Vi says "Maybe a few more for e and tau in there, too"
The subtitles say "E and [towel]" instead!
Tau is not a towel!(4 votes)
Is it possible for pi to be written as a fraction?(3 votes)
Nope. There are a ton of ways to prove this and if you're interested you can do a quick search on "pi irrationality proof".(2 votes)
You just say Pie isn't real food? TRIGGERED!(3 votes)- pie is not what you think it is she is right(3 votes)
2:40Video transcript
Voiceover:Hello and welcome
to that one day of the year when, well, everyone else
is building up how great Pi is. I'm here to tear it down,
because you deserve the truth. Forget about the part where Pi
isn't the correct circle concept. This Pi day, I'm not
about how people worship Pi for being infinite
for going on forever. First of all, Pi is not infinite. It is more three, but
you know, less than four. There are cultures where
three is the biggest number, so I don't want to be insensitive, but trust me on this four is
not infinite and neither is Pi. I know it's not about it's magnitude, it's about all those digits, infinite digits going on forever, but first of all it doesn't go anywhere. It just is. There's no time element. If you had a number
line, Pi would be exactly one point on that number line sitting perfect still right now. It's not going to start wondering off on an infinite journey that takes forever, or even on a finite
journey that takes forever, or an infinite journey
that takes finite time. Pi is a number not a process. Secondly, yeah, so it's
got infinite digits. So what, one-third has infinite digits. There's exactly as exactly as many digits in one-third and in Pi
as in 99.9999 repeating. Oh, and there's also as
many digits as in numbers like, say, five, I know, big number. It's even more than four, so, it's
piratically like double infinity. Which, it actuality kind of is,
because in decimal innovation there's secretly infinite
zeros in all of these places. Zero's going out to forever. Ooh! So mysterious, and then
zero's going the other way too. Which is actually not any more zeros than if they only went one way. No. Pi is not especially
infinite in any way, it's more like in-between-finite. There's an infinite number
of rational numbers. for any two factions you
can find another fraction that's between them again
and again and again. There's never any fractions that are right next to each other on the number line. But, despite there's a infinite
amount of rational numbers, Pi isn't one of them. Take any rational number, and you can find an
infinite number of rational numbers that are closer
to Pi on either side. Pi is between all of
them in one of the gaps. It isn't infinite. It's in-between-finite. So what, you think that's special, as if there's just one
hole in the rational number line exactly where Pi is, and once you plug that in
with a super special number, you're good to go? Maybe, a few more for E and
[towel] and square root too. No! Super nope! The in-between-[finiteness] of Pi, its irrationality is an
incredibility un-special property. Turns out, most real
numbers are irrational. It's the nicely packaged
rational numbers that are weird. In fact, if you threw a
dart and picked a random number off the number line, the chance of getting a
rational number is exactly zero. I'll get into kinds of
infinities some other time, but [unintelligible] to say the number of rational numbers, like the
number of digits in Pi, is the small and unimpressive
countable infinity. While the number of
irrational numbers is so much bigger than countable infinity, that when you compare the two, cantabile infinity looks like zero. So, I don't know why
anyone would make a fus about the grand infinities and forever, as about the boring little number like Pi. And of course, those are
just the first couple of kinds of infinities
in an infinite number of infinities in their correspondingly more in-between-[finiter] numbers
like the [infinitesimals]. So, don't let Pi impress
you by being a member of an unaccountably infinite set of
in-between-infinite number either. The only thing even a
little weird about Pi is that you do get an
irrational number by taking such a simple ratio of such
a simple geometric object. Surely that never happens
with other simple ratios of other simple geometric objects. Oh wait! Their in everything!
What are the chances? No! Let's pretend math equals arithmetic, and then get all surprised
and amazed when the moment you leave arithmetic that you
get a non-arithmetic number as if it were some odd
unpredictable phenomenon. That way, by the time you get to calculus you won't have any idea what's going on and memorize just enough symbol shuffling to pass your class without
ever realizing that you were dealing with
infinities two levels deeper than the infinity you think
is so cool when Pi does it. Pi is not special. Yeah, Pi can be fun, and I'd
never deny you your deserts, but maybe try some real
food once in a while.