In 2015, I was in Arizona and I posted a Facebook video celebrating Pi day at 9:26 am local time to celebate 3.1415926. It was cool. Now I have to way 96 years to be able to post another similar video.

Well, I think we can safely assume that Pi day is quite popular in the US, but not nearly so in Europe or most other parts of the world. This can be expected as the relation between pi and "3/14" for the 14th of March is obvious where this date format is used, but not quite so elsewhere. If you take a look at this map it seems logical that this day may be much more popular in the US than elsewhere.

Aaand just to continue; I took a picture on the 11th november 2011 at 11:11:11, aperture f/11 and 1/10s. (Since 1/11th is not an option on the camera). Though the exif says 11:11:11:11:11:11
And, I also have a geocaching souvernir because I found a cache at March 14th 2015 (which in European terms mean 14.03.2015 and has nothing to do with Π).

This must be one of the least known ways to compute Pi (no circles, trigonometry or integrals in sight). Here's my implementation for the HP-71B, a user-defined function trivially easy to convert to RPN, RPL or whatever: 1DEF FNP(N) 2 T = N 3FOR I = N-1 TO 2 STEP -1 4 T = CEIL(T/I)*I 5NEXT I 6FNP = N*N/T 7END DEF

It would easily fit in just one line but this way its simplicity might be even clearer.
Let's see the function's value for N = 10, 100, ..., 1000000:
DESTROY ALL @ FIX 5

The band used the number Pi to create the songs rhythms that starts at 1:08 in the video. Keep in mind that everything before 1:08 does not use Pi in any way. It's quite interesting how they created the rhythms and they explain the how they did it in the video's description.

They used 71 digits of Pi to do it. It's a fantastic song and a top favorite of mine. I mainly sharing it because of how After the Burial's amazing use of Pi in music and it's Pi day. It's really cool!

(03-15-2019 04:31 AM)Carsen Wrote: [ -> ]They used 71 digits of Pi to do it. It's a fantastic song and a top favorite of mine.

Great, thanks for the reference, I didn't know about this song or this group !

To reciprocate, I'd recommend the song "PI" (Greek character, actually) from Kate Bush's 2005 double album "Aerial", in which she sings up to the 78^{th} decimal place of Pi, and after that from the 101^{st} to the 137 ^{th}. It was played in a major Spanish radio station as part of Pi day celebrations !

I find the song beautiful, atmospheric, evocative, and the whole "Aerial" album is a marvel to behold, very recommended.

(03-15-2019 05:07 AM)Valentin Albillo Wrote: [ -> ]I find the song beautiful, atmospheric, evocative, and the whole "Aerial" album is a marvel to behold, very recommended.

Totally agree. That album is a masterpiece. I love Peter Erskine's drumming and the musicianship that oozes out from the album (needless to say Kate's voice, improving with age like the best wines).

This must be one of the least known ways to compute Pi (no circles, trigonometry or integrals in sight). Here's my implementation for the HP-71B, a user-defined function trivially easy to convert to RPN, RPL or whatever: 1DEF FNP(N) 2 T = N 3FOR I = N-1 TO 2 STEP -1 4 T = CEIL(T/I)*I 5NEXT I 6FNP = N*N/T 7END DEF

It would easily fit in just one line but this way its simplicity might be even clearer.
Let's see the function's value for N = 10, 100, ..., 1000000:
DESTROY ALL @ FIX 5

(03-15-2019 05:07 AM)Valentin Albillo Wrote: [ -> ]To reciprocate, I'd recommend the song "PI" (Greek character, actually) from Kate Bush's 2005 double album "Aerial", in which she sings up to the 78^{th} decimal place of Pi, and after that from the 101^{st} to the 137 ^{th}.

Interesting! (I like exploring new styles). After listening to the entire song, your description describes it perfectly. Especially the word "atmospheric.

I like how there's another song about Pi. Pretty cool.

Sum of reciprocals of integers (limit of course) from One to Infinity (not starring Deborah Kerr and Frank Sinatra) is Pi^2/6.

Probability that two random (will define below) integers are co-prime is 6/Pi^2.

How to uniformly choose an integer at random.
1. Choose a large (not necessarily specified) integer: X.
2. Choose an integer within 1 to X with probability 1/X (using come criterion).
3. If the density of integers satisfy that criterion has a limit as X goes to infinity, the will choose an integer with the proper density.

Example: Choose even integer within 1-x. Probability is either 1/2 or 2X/(2*X+1) which has a limit 1/2 so we can meaningfully say that half of all integers are even.

(03-16-2019 04:23 PM)ttw Wrote: [ -> ]Sum of reciprocals of integers (limit of course) from One to Infinity (not starring Deborah Kerr and Frank Sinatra) is Pi^2/6.