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Happy Pi day everyone!!
03-14-2019, 12:25 PM
Post: #1
Happy Pi day everyone!!
Happy Pie day!

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.

Namir
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03-14-2019, 12:34 PM
Post: #2
RE: Happy Pi day everyone!!
A holiday not celebrated in Europe.
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03-14-2019, 01:30 PM (This post was last modified: 03-14-2019 01:32 PM by Eddie W. Shore.)
Post: #3
RE: Happy Pi day everyone!!
Happy Pi Day!

May all the slices of 335/113 or 3.1415926535 be excellent!

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03-14-2019, 03:53 PM
Post: #4
RE: Happy Pi day everyone!!
(03-14-2019 12:34 PM)ttw Wrote:  A holiday not celebrated in Europe.

Says who ?

Celebraciones del dia de Pi hoy en España

V.

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03-14-2019, 08:09 PM
Post: #5
RE: Happy Pi day everyone!!
(03-14-2019 03:53 PM)Valentin Albillo Wrote:  
(03-14-2019 12:34 PM)ttw Wrote:  A holiday not celebrated in Europe.

Says who ?

Celebraciones del dia de Pi hoy en España

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.

Dieter
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03-14-2019, 08:58 PM (This post was last modified: 03-14-2019 08:59 PM by Gerson W. Barbosa.)
Post: #6
RE: Happy Pi day everyone!!
Just for the occasion, yet another wp34s \(\pi\) program. Optimization and conversion to HP calculators are left as an exercise for the reader.

0001 **LBL A
0002 RCL X
0003 # 012
0004 [sqrt]
0005 .
0006 7
0007 5
0008 RCL[times] Y
0009 RCL[times] Y
0010 [sqrt]
0011 ||
0012 STO+ X
0013 RCL L
0014 DSE Z
0015 BACK 006
0016 RCL[times] Y
0017 [sqrt]
0018 R[^]
0019 INC X
0020 # 072
0021 [times]
0022 RCL Y
0023 1/x
0024 [cmplx]CONJ
0025 +
0026 DEC X
0027 # 036
0028 /
0029 2[^x]
0030 # 002
0031 +
0032 STO[times] Y
0033 INC X
0034 R[v]
0035 +
0036 RCL/ Z
0037 END

 4 A --> 3.141592653668149565494622891088879

20 A --> 3.141592653589793238462643383279505
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03-14-2019, 10:12 PM
Post: #7
RE: Happy Pi day everyone!!




He uses the solution of the Basel problem and a bunch of his new book to calculate an estimate of \(\pi\):

\(\sum_{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi^{2}}{6}}\)

BTW: Basel is a town close to Allschwil, as some of you may know.

Cheers
Thomas
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03-14-2019, 10:34 PM
Post: #8
RE: Happy Pi day everyone!!
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 Wink
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).

Esben
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Elektronika MK-52 & MK-61
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03-15-2019, 12:45 AM
Post: #9
RE: Happy Pi day everyone!!
 
Hi, all:
       
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:

       1   DEF FNP(N)
       2       T = N
       3       FOR I = N-1 TO 2 STEP -1
       4             T = CEIL(T/I)*I
       5       NEXT I
       6       FNP = N*N/T
       7   END 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

FNP(10)          -> 2.94118
FNP(100)         -> 3.09215
FNP(1000)        -> 3.13903
FNP(10000)       -> 3.14133
FNP(100000)      -> 3.14153
FNP(1000000)     -> 3.14159

The limit for  N -> Inf   is exactly Pi, of course.

Happy  Pi  Day ! Smile

V.
 

  
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03-15-2019, 04:31 AM
Post: #10
RE: Happy Pi day everyone!!
On Pi day, I always celebrate it by blasting the song Pi by After the Burial.

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!
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03-15-2019, 05:07 AM
Post: #11
RE: Happy Pi day everyone!!
(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 78th decimal place of Pi, and after that from the 101st to the 137 th. It was played in a major Spanish radio station as part of Pi day celebrations ! Smile

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

Regards.
V.
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03-15-2019, 06:35 AM
Post: #12
RE: Happy Pi day everyone!!
(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).
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03-15-2019, 07:09 AM
Post: #13
RE: Happy Pi day everyone!!
I don’t celebrate until 15:00 hours:

3.1415

3rd month/14 day/15 hours
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03-15-2019, 08:35 AM
Post: #14
RE: Happy Pi day everyone!!
... as usually I'm always late ... Smile





Csaba
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03-15-2019, 05:11 PM
Post: #15
RE: Happy Pi day everyone!!
(03-15-2019 12:45 AM)Valentin Albillo Wrote:   
Hi, all:
       
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:

       1   DEF FNP(N)
       2       T = N
       3       FOR I = N-1 TO 2 STEP -1
       4             T = CEIL(T/I)*I
       5       NEXT I
       6       FNP = N*N/T
       7   END 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

FNP(10)          -> 2.94118
FNP(100)         -> 3.09215
FNP(1000)        -> 3.13903
FNP(10000)       -> 3.14133
FNP(100000)      -> 3.14153
FNP(1000000)     -> 3.14159

The limit for  N -> Inf   is exactly Pi, of course.

Happy  Pi  Day ! Smile

V.
 

What the heck!? How does that even work?
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03-16-2019, 06:27 AM
Post: #16
RE: Happy Pi day everyone!!
(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 78th decimal place of Pi, and after that from the 101st 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.
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03-16-2019, 07:50 AM
Post: #17
RE: Happy Pi day everyone!!
(03-15-2019 05:11 PM)mpark Wrote:  How does that even work?
Indeed - a clue would be nice! Please?
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03-16-2019, 03:18 PM
Post: #18
RE: Happy Pi day everyone!!
(03-16-2019 07:50 AM)EdS2 Wrote:  Indeed - a clue would be nice! Please?

A002491
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03-16-2019, 04:23 PM
Post: #19
RE: Happy Pi day everyone!!
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.
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03-16-2019, 05:11 PM
Post: #20
RE: Happy Pi day everyone!!
(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.

You missed a "squared" somewhere …

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