Poll

1 vote (6.25%)
No votes (0%)
No votes (0%)
1 vote (6.25%)
No votes (0%)
2 votes (12.5%)
5 votes (31.25%)
3 votes (18.75%)
1 vote (6.25%)
8 votes (50%)

16 members have voted

Wizard
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Wizard
Joined: Oct 14, 2009
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March 14th, 2019 at 7:03:38 AM permalink
Today is March 14, which can mean only one thing -- It's pi day!!!

Pi day is the day when we celebrate all that is elegant and beautiful about not just pi, also known as Archimedes' Constant, but all mathematics. I just want to dance through the streets, singing "I love math," but I'm afraid that the day would become associated with the number 5150, as opposed to 314, for me if anyone called the police.

The assignment for the readers is to ponder the wonder and simplicity of the equation 1 + e^(pi*i) = 0. All the most significant constants in math right there in one equation. Better yet, for extra credit, prove that equation. Hint: Use Taylor's Expansion.

The question for the poll is how to you feel about pi day?

It's not whether you win or lose; it's whether or not you had a good bet.
odiousgambit
odiousgambit
Joined: Nov 9, 2009
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March 14th, 2019 at 7:46:13 AM permalink
I do OK with remembering numbers although very limited in math ability it seems. Not to say I am a prodigy who memorizes huge long numbers that can amaze one and all.

without trying to go crazy with it I've got pi memorized to this now:

3.141592653589 [from memory, check that]

obviously that is no big deal. Just saying. It'll keep growing, see you next year.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
gamerfreak
gamerfreak
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March 14th, 2019 at 7:48:10 AM permalink
Google has broken the word record by calculating Pi to 31.4 trillion digits

https://cloud.google.com/blog/products/compute/calculating-31-4-trillion-digits-of-archimedes-constant-on-google-cloud
AZDuffman
AZDuffman 
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Thanks for this post from:
onenickelmiracle
March 14th, 2019 at 8:38:33 AM permalink
One slice of cherry ala mode, please.


On a more serious note, how do they figure the two ratios exact enough to calculate out all those places without error. IOW, if they round the fractional measurement just a touch, it would be off, no?

I'll donate $20 to your favorite charity if you can get yourself thrown out of Circus Circus for singing "I Love Math!"
Tolerance is the virtue of believing in nothing
tringlomane
tringlomane
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March 14th, 2019 at 8:44:14 AM permalink
Happy pi day!
CrystalMath
CrystalMath
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tringlomane
March 14th, 2019 at 11:22:11 AM permalink
In recognition of pi day, here is my contribution. I've never seen this anywhere, and if so, I independently discovered this a few days ago. It started with calculating pi using a series for calculating the arctangent of 1, which gives pi/4. Then, I realized that this estimate alternates above and below pi/4, so I thought I should average two adjacent estimates. Then, when I charted those, they still alternate above and below pi/4, so I averaged those. You can see where this is going - keep averaging the adjacent results until you get down to one result. Turns out, this is much faster with Pascal's Triangle.

So, I calculated the first 51 terms of the series, then weighted each term by the Triangle values. Here are my results:

Term NumberTermCumulative ValueMultiplierContribution to pi/4
0+1/1118.88178E-16
1-1/30.666666667502.96059E-14
2+1/50.8666666671,2259.42949E-13
3-1/70.72380952419,6001.26003E-11
4+1/90.834920635230,3001.70781E-10
5-1/110.7440115442,118,7601.40011E-09
6+1/130.82093462115,890,7001.15865E-08
7-1/150.75426795499,884,4006.6915E-08
8+1/170.813091484536,878,6503.87718E-07
9-1/190.7604599052,505,433,7001.69223E-06
10+1/210.80807895210,272,278,1707.3726E-06
11-1/230.76460069137,353,738,8002.5367E-05
12+1/250.804600691121,399,651,1008.67557E-05
13-1/270.767563654354,860,518,6000.00024192
14+1/290.802046413937,845,656,3000.000668084
15-1/310.7697883492,250,829,575,1200.001538913
16+1/330.8000913794,923,689,695,5750.003498892
17-1/350.771519959,847,379,391,1500.006747891
18+1/370.79854697718,053,528,883,7750.012804505
19-1/390.77290595230,405,943,383,2000.020873023
20+1/410.79729619647,129,212,243,9600.03337414
21-1/430.77404038267,327,446,062,8000.046286674
22+1/450.79626260488,749,815,264,6000.062765934
23-1/470.774986008108,043,253,365,6000.074368964
24+1/490.795394171121,548,660,036,3000.085868286
25-1/510.775786328126,410,606,437,7520.087101544
26+1/530.794654253121,548,660,036,3000.085788407
27-1/550.776472435108,043,253,365,6000.074511604
28+1/570.79401629488,749,815,264,6000.062588867
29-1/590.77706714267,327,446,062,8000.046467671
30+1/610.79346058447,129,212,243,9600.033213585
31-1/630.77758756830,405,943,383,2000.020999454
32+1/650.79297218418,053,528,883,7750.012715114
33-1/670.7780468119,847,379,391,1500.006804976
34+1/690.7925395644,923,689,695,5750.003465867
35-1/710.7784550572,250,829,575,1200.001556239
36+1/730.792153687937,845,656,3000.000659844
37-1/750.778820354354,860,518,6000.000245468
38+1/770.791807367121,399,651,1008.53763E-05
39-1/790.77914913937,353,738,8002.58497E-05
40+1/810.79149481810,272,278,1707.22129E-06
41-1/830.7794466252,505,433,7001.73448E-06
42+1/850.791211331536,878,6503.77284E-07
43-1/870.77971707899,884,4006.91727E-08
44+1/890.79095303415,890,7001.11633E-08
45-1/910.7799640232,118,7601.46777E-09
46+1/930.790716711230,3001.61739E-10
47-1/950.78019039519,6001.35818E-11
48+1/970.7904996731,2258.60078E-13
49-1/990.780398663503.46567E-14
50+1/1010.79029965317.01927E-16
Total1,125,899,906,842,6200.78539816339744900


ValueNumber
pi/4 estimate0.78539816339744900
pi estimate3.14159265358979000
pi() - excel function3.14159265358979000


With very little computation, I was able to generate pi to the same precision as Excel.

Happy pi day, and thanks, Miplet, for the table generator.
I heart Crystal Math.
unJon
unJon
Joined: Jul 1, 2018
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March 14th, 2019 at 12:23:42 PM permalink
I sort of expected Wizard to be a Tau day snob and snub Pi day. I’m happy to see that’s not the case.

Enjoyed reading this article today:

https://fivethirtyeight.com/features/even-after-22-trillion-digits-were-still-no-closer-to-the-end-of-pi/amp/
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Ayecarumba
Ayecarumba
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March 14th, 2019 at 12:42:01 PM permalink
Here's my Pi Day pondering:

Amongst all the currently known digits, how long is the longest sequence of the same number (e.g. 1111 or 333333)?
When I die, I want everyone who ever worked with me on a group project to lower me into my grave so they can let me down one last time.
Ayecarumba
Ayecarumba
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March 14th, 2019 at 12:58:56 PM permalink
Am I the only one who feels it is unfair that 0.999...(repeated to infinity) getting rolled up to "1" is the bastard daughter while pi gets to be the golden child?
When I die, I want everyone who ever worked with me on a group project to lower me into my grave so they can let me down one last time.
Wizard
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Wizard
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Thanks for this post from:
Ayecarumba
March 14th, 2019 at 2:52:21 PM permalink
Quote: Ayecarumba

Here's my Pi Day pondering:

Amongst all the currently known digits, how long is the longest sequence of the same number (e.g. 1111 or 333333)?



I know they discovered eight consecutive 8's, but this is old news. Perhaps they have broken the record since then.

In thinking about this more, I calculate about a 96% chance there are at least 14 consecutive equal digits in 31.4 trillions digits, somewhere.
It's not whether you win or lose; it's whether or not you had a good bet.

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