Pi is approximately 355/113 (pi day short)

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.

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[Info_rare]

Physicists: Wow! Pi=355/113
Mathematicians: bro, zoom in!

[Real_Azure]

fun fact, 3.141/1 is also a very close estimate of pi!!!1

[dvx-zeqz]

Another approximation is 22/7, and clearly you can see how the spikes are really close already at 22th

[mamatadash]

Since pi is a continued fraction, we can cut the fractions at different points and it will give us different approximations of pi

[_Cynther_]

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!

[elegy]

Pretty cool how the 22nd spike almost lines up on the 7th rotation to demonstrate the 22/7 estimate of pi

[Bhuvan_MS]

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.

[yatminghui]

Alright, BUT NOW GIVE ME BACK MY DONUT!

[Random.]

No one:
My brain: YOU SPIN ME RIGHT ROUND BABY RIGHT ROUND LIKE A RECORD BABY RIGHT ROUND ROUND ROUND

[tamirerez]

Great animation, but how does it prove that π is 355/113??

[stalinexpress]

Thx for my new eyes I ordered btw what took you soo long to make this

[izzabelladogalini]

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 🤣

[ThR.]

"Never let them know your next move."
*Draws a perfect eye using science*

[estudematematica]

This is truly gorgeous.
Isso é realmente lindo.

[brandontechnerd]

If you were wondering how precise 355/113 is:
355/113 = 3.141592920354
Pi = 3.141592653589

[tanishkaaa]

looks like eye pupil
math is interconnected with everything damn

[KingNinja]

Me not understanding this but listening to the music

[hevad]

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.

[winogronko]

Interesting, but i still think the chemistry is more interesting, but tho i like math.

[Tomzin]

mathematicians trying to come up with the hardest ways to find shit they alread knew: