Pi is approximately 355/113 (pi day short)
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- čas přidán 4. 03. 2023
- This short animation shows the beginning of the creation of the hypocycloid where the ratio between the radii of the two circles is Pi. Because Pi is irrational, the hypocycloid will never close, so we end after 113 revolutions. As a byproduct, it appears that the curve almost closes up, and there are total of 355 intersection points between the circle and the hypocycloid (spikes). This means this visual shows that Pi is roughly 355/113, which is one of the best simple approximations of the circle constant.
If you like this video, check out my others and like and subscribe!
To see a slower version of this video (with not quite 113 revolutions), see • Pi Hypocycloid
If you want to see more hypocycloids, check these:
• Drawing Hypocycloids (...
• Nested Powers of 2 Hyp...
#manim #hypocycloid #spirograph #circle #rollingcircles #irrational #Pi #mathvideo #math #mtbos #animation #iteachmath #mathematics #piday
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Physicists: Wow! Pi=355/113
Mathematicians: bro, zoom in!
😀
Really you deserve more subscribers, you work hard
@@Info_rare :) Thanks!
Pi = 3
@@debmalya6144 pi=e=3
fun fact, 3.141/1 is also a very close estimate of pi!!!1
3.14159265358979/1 is also a good estimate
π/1 is a gud estemate!1!111!!1!1!1!!1!1!one!1!1!11!uno!1!!1!1!1!111!!!!1!1!
3.141592653589793236/1 is more accurate
@@Anti_Racist696 and 3.141592653589793238462643350288419716939937510/1
pi/1 is veeryy gud
Another approximation is 22/7, and clearly you can see how the spikes are really close already at 22th
Definitely!
22th? Or 22nd
@@hemavarma5436 oops my bad
Now the thing is, my birthday is July 22nd, which in Europe is shown as 22.07.
another approximation is 21/7 which is way easier to remember
This is why i love math
👍😀
*meth
I agree. This is a satisfying visualization.
@@user-sg5ii6zy1q beat me to it
@@user-sg5ii6zy1q
*Jesse, stop making memes here and go to the kitchen now!*
For this pi day (2024) there was recently a contest at my highschool where students could enter to try to recite as many digits of pi as they could. I entered and set the record of 1,234 digits of pi, nearly quadrupling the previous school record 🤭🤭. The next day the local news showed up and interviewed me it was so cool!
Since pi is a continued fraction, we can cut the fractions at different points and it will give us different approximations of pi
Everything is a continued fraction. Cuting it off at different point gives the best fractional approximation with that amount of digits
@@pauselab5569 yes but some go infinitely long and some ar finite.
Pretty cool how the 22nd spike almost lines up on the 7th rotation to demonstrate the 22/7 estimate of pi
Alright, BUT NOW GIVE ME BACK MY DONUT!
no, i will keep performing approximate pi equations on it
Since a true line/curve does not have any thickness(it is 1D), the circle will be filled with infinite lines taking infinite revolutions.
The fraction p/q cannot be defined taking infinities on both numerator and denominator. Hence, it also explains that pi is irrational.
52163/16604 be like: hold my 🍻
Makes pupil cutely
Very satisfying, thank you 😊
Thanks for watching
that was wonderful
Glad you liked it!
Groovy! ^.^
👍
reminds me of meatspin
Good video bro
If you were wondering how precise 355/113 is:
355/113 = 3.141592920354
Pi = 3.141592653589
Difference: 0.000000266764
That’s an amazing eye drawing
No one:
My brain: YOU SPIN ME RIGHT ROUND BABY RIGHT ROUND LIKE A RECORD BABY RIGHT ROUND ROUND ROUND
"Never let them know your next move."
*Draws a perfect eye using science*
This is truly gorgeous.
Isso é realmente lindo.
👍😀
355/113 takes you accurately to 6 decimals. ...which is as close as most people will ever need, if you want more accuracy you can get to 9 decimals but the fraction gets rather large..
13307663182/423595077
If you want more than 9 decimals...do it yourself I've had enough 🤣
:)
8717442233⁄2774848045
There’s a typo in your numerator. It should be 1330763182, which gives you 13 decimals actually.
For this accuracy I need an even larger fraction:
6155147411456/1959244271985
I got this by using a correction factor I have found for the Wallis Product.
Submit the following to WolframAlpha:
Product((4k^2)/(4k^2 - 1),{k,1,n})*(2 + 4/(8n + 3 + ContinuedFractionK[4k^2 - 1,8n +4,{k,1,n}]))
That’s what we get when n=6.
looks like eye pupil
math is interconnected with everything damn
Thx for my new eyes I ordered btw what took you soo long to make this
ZOOM IN ZOMM IN ZOOM IN
Check this out: czcams.com/video/DC8JlortDqE/video.html
Thanks for explaining
Latrice Royale vs Trinity The Tuck
Great animation, but how does it prove that π is 355/113??
The ratio of the two circles is given by pi. If the ratio between the two circles is a rational p/q then the cycle closes up after q revolutions and p cusps. This one almost closed up after 113 revolutions and 355 cusps so pi is nearly 355/113. You can also see at the beginning that it almost closes after 7 revolutions and 22 cusps so pi is roughly 22/7 too!
@@MathVisualProofs
Wow, beautiful.
After 25 years of teaching math, these visual proofs are still new to me. Amazing.
@@tamirerez2547 Glad you are enjoying them! I learn new ones every day too :)
That the ratio of the two circles is Pi is assumed by construction, it could have been any other number. This is a visual way to see how well a fraction can approximate any number. If by construction you had chosen that bigger radius was square root of two times the other, instead of Pi, we could have seen its rational approximation counting spikes and revolutions. Am I right?
Anyway, I can't stop watching and listening :)
@@MathVisualProofs thank you for this explanation, I’ve seen 355/113 repeated countless times but nobody could demonstrate why it approximates pi or how.
very interesting👍
Fun to “see” the approximation.
@@MathVisualProofs HHSHA I GET UR JOKE
@@xyovirxI don’t get it
@@Xlebywek_Memep same i forgot how i got it
The song is perfect lol
You spin me right round, baby, right round, in a manner depriving me of an inertial reference frame baby, right round.
Hi! I have a question - what is the ratio between radiuses of those two circles? How was it determined? And is this the only proportion that would give this result or could this be replicated with any two different circles?
The ratio between the two circles is pi. So that is why it rolls almost together at 355/113. If I had made the ratio 355/113 it would close up perfectly.
The initial pitcher makes me think of a roll of Teflon tape
That's why I love math. There's always room for debate
i'm just vibing to the song
Today's lesson: how to create a black hole
WoW
Spirograph love!!!
😀👍
113355 is the smallest rational approximation of pi that has more digits on the output (7) than on the input (6).
really beautiful 😍
Interesting , but i still think the chemistry is more interesting , but tho i like math.
Lovely
Me not understanding this but listening to the music
Very cool
😀👍
I don't understand what this mean but this shit is funny af idk why
Very, very cool! ❤
Thanks!
Engineers: It's close enough.
Damn cool
my brain hurts
Waaaa
mathematicians trying to come up with the hardest ways to find shit they alread knew:
The question is: does the result get better if the small circle spin round the outer perimeter of the big circle?🤔
U spin me right round
excellent video
Glad you liked it!
THE SONGGGGG
My favourite Pi value
You know IT IS over when you See a Video about math
but why?
@@MathVisualProofs
Because I hate Mathe, I'am so Bad in it.
@@ameliekruger1561 but you could possibly be good. Just give it another try 😀
@@MathVisualProofs
Oh believe me I am trying, but I Just dont Like it. Iam more interested in Reading, drawing Stuff Like that math isnt my thing
Wonderful
Thank you
Nice
This is why I love math… because of complex numbers like pi!
Can you make it keep going and see if there’s any visual indication of the inaccuracy?
There is. If you continue it starts a new cycle that is not overlapping.
Can you do
Ramanujan Summation?
1+2+3+4+...=-1/12
It’s unfortunately not true and so a geometric visualization isn’t possible.
π = 62832/20000 .(this was stated by aryabhata). Which is very close to value of π
Rly cool nex can u try 22/7
What's the formula to get more digits
It's correct til 3.141592
So this how human eyes are made, good to know
I guess the distracting factor here is that this is running inside a circle. Makes you think that the mechanism by which it is approximating pi has something to do with the circle, and is not.
Makes for a nice animation, and is easier to see in a non-moving reference frame (it could have been done to roll over a straight line marked every pi). That's alright, I just wish it was made clearer at the beginning that the circles were proportional to each other by PI, because I kept thinking you can easily decide a diameter of the inner circle that matches the mark perfectly.
3 blue 1 brown’s logo
Or is it 3 blue 1 blue?
Hi, what actually is pi? Is it the ratio of the diameter to the circumference? Or smth else
Take any circle: divide circumference by diameter. That’s pi
France be like：
Did you know that pi is the best approximation of pi. It's so accurate, that it is equal to itself 😱😱😱
😆
That’s closer than 22/7 is
We love hypociloid
spirograph
This equation is slightly more than pi, but I'm impressed that it's very close
Happy pi day
To you too!
mathspin
Is the diameter of the smaller circle 1/3 of the bigger circle?
No. Pi is the ratio between the two radii
I compared it to 22/7 with (355/22) / (113/7) and 355/113 is 99.96% of 22/7
another close number is the cubic root of 31.
3.14
ПОНЧИК
104348/33215, hallo
How does that prove that 355/113 ≈ π
The ratio of the two circles is Pi. It is known that if the ratio were 355/113 then the hypocycloid would close up after 113 rotations and 355 spikes. This one almost closes up at the same time (though not quite ). If you watch early you will see that after 7 rotations and 22 spikes it almost closes up too. That gives the 22/7 approx
what is radius of new circle?
The ratio of the two shown circles is Pi (so big circle radius/rolling circle radius is Pi). Then the newly created "inner circle" has a radius obtained by taking big circle radius and subtracting the diameter of the rolling circle (and the diameter of the rolling circle is two times big circle radius/Pi).
@@MathVisualProofs
π = 2 in Riemann Paradox And Sphere Geometry Mathematical Systems Incorporated
Video about pi: no
Video about making circle inside circle = *yes*
How does this work?
Spirograph!
Upto 6th decimal
not good music.
anyway, awesome video
ah yes
4blue0brown
hah!
Only 6 digit correct
No zoom in or anything?
If you want a Hypocycloid zoom, check this out: czcams.com/video/DC8JlortDqE/video.html :)
@@MathVisualProofs I kinda meant a zoom in to see how close 355/113 is to pi
Cause being this zoomed out it just makes me think they're exactly the same, cause there's no noticeable difference between the two points
@@xanderlastname3281 oh! I see. Yes it is hard to see. Even with zoom because the thickness of the dot :)
3.14156
acos(0) = pi
π≈3.14
Rotary engines in a nutshell
Ha! The Hadron Collider and The Birth of Calculus 💯
😃👍
Vsause
Eye
355/133 is actually only 0.000008% greater than pi. If you used both numbers to calculate the circumference of the Earth the difference would be a little over 3 meters.
π ≈ 355/113