Pretty much going to be the same as all the other pi days i suppose but shouldn’t pass by without notice.
Wasn’t the only true Pi day back in 1592?
In honor of Pi day, I give you the Wallis Product:
pi/2 = (2/1)(2/3)(4/3)(4/5)(6/5)*…
Looks cool, but converges a bit too slow for my taste. At n = 100, it has pi = 3.1206079
It depends. If we’re talking about truncating it at the sixth digit to the right of the decimal point, then 1592. But if were talking about rounding it at the sixth digit, then 1593.
Of course soon enough it’ll be the year 15926 and we can really party down.
Then, ref @Crafter_Man, do it all again in 15927! W00t!!
I’ve made my reservations. How about y’all?
I will have a slice of pecan, blueberry, and apple. My favorite pi(e)s.
It’s probably a good thing the value of pi is 3-something, not 7-something. Seven slices of any flavor(s) would be a lot.
In a now annual tradition, Matt Parker has posted a calculating π video to his Stand-up Maths channel.
The TLDV version: You have a wall, mass2, mass1 on a 1-d frictionless surface. If you slide mass1 towards mass2 and bounce it (perfectly), mass2 bounces against the wall, comes back and hits mass1, etc. The total number of collisions gives you the first x digits of π if mass1 has a certain square power of 10 times more mass than mass2. E.g., if they are equal there are 3 bounces. If mass1 is 100 times more than you get 31 bounces, etc.
Experiments on an air table and formulas on a white board ensue. :Large number of digits of π do not.
Guest stars Steve Mould and 3Blue1Brown. The latter had done a video on this that inspired the test.
It is also Einstein’s birthday–as well as my anniversary (61st). Wallis’s product is really quite amazing. Another formula is
\pi^2/6=1+1/4+1/9+1/16+1/25+\cdots
And \pi^4/90=1+1/16+1/81+1/256+1/1225+\cdots
Similar formulas are known for the sums of reciprocal nth powers for all even n. For odd n, essentially nothing is known.
Thanks to Euler, who is credited for popularizing \pi as the symbol for the number we celebrate today.
For the math geeks out there, the 3Blue1Brown video is a must watch. They plot the conservation of momentum and conservation of energy on a circular plot, which is how PI comes out of it. Linking to that section here.
I always liked \frac{\pi}{4} = \frac{1}{1}-\frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \ldots
Pi Day is for hanger-ons, amateurs, and wannabes. Speaking for myself, I am giddy with excitement that Tau Day - June 28 - is less than four month away.
Hear, hear
In honor of Pi day, I texted my lovely wife a heartfelt message:
3.14159
To which she squee’d with joy (yes, I could have had more digits, but this is more than enough for almost anything in the Newtonian world)!
She brought home a $1.99 mini-blueberry pie that her office handed out to all the engineers.
'Tis a day of much love!
The third video in the series is the really interesting one. They convert the problem into a problem with light bouncing off of mirrors at an angle to each other.
Tau day has two critical problems, compared with pi day. First, it’s not during the school year, so you can’t celebrate it with your classes. Second, there’s no dessert named taue that you can justify binging on.
For Math Club, Wal-Mart had a great price (something like 79 cents) on single-serving individual pies, and we calculated that we’d need about 40 of them. We ended up using 39, with the last one currently sitting in my fridge awaiting lunch. We also had some videos playing, and a contest for memorizing digits (the winner had 62 digits past the decimal point).
Just take the day to play Warhammer 40k!
And sup upon silken tofu in ginger syrup!
(I apologize to any who feels that I’m cheating by using the English transliteration to get “Tau” to work, it’s a fair cop!)
Why not eat two pies on tau day? Too bad December does not have 56 days.