Thread Rating:

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
Administrator
Wizard
  • Threads: 1491
  • Posts: 26435
Joined: Oct 14, 2009
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?

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
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
  • Threads: 57
  • Posts: 3540
Joined: Dec 28, 2014
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
  • Threads: 240
  • Posts: 13885
Joined: Nov 2, 2009
Thanked by
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!"
All animals are equal, but some are more equal than others
tringlomane
tringlomane
  • Threads: 8
  • Posts: 6281
Joined: Aug 25, 2012
March 14th, 2019 at 8:44:14 AM permalink
Happy pi day!
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1909
Joined: May 10, 2011
Thanked by
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
  • Threads: 14
  • Posts: 4574
Joined: Jul 1, 2018
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
  • Threads: 236
  • Posts: 6763
Joined: Nov 17, 2009
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)?
Simplicity is the ultimate sophistication - Leonardo da Vinci
Ayecarumba
Ayecarumba
  • Threads: 236
  • Posts: 6763
Joined: Nov 17, 2009
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?
Simplicity is the ultimate sophistication - Leonardo da Vinci
Wizard
Administrator
Wizard
  • Threads: 1491
  • Posts: 26435
Joined: Oct 14, 2009
Thanked by
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gamerfreak
gamerfreak
  • Threads: 57
  • Posts: 3540
Joined: Dec 28, 2014
Thanked by
Ayecarumba
March 14th, 2019 at 3:01:03 PM permalink
Quote: Wizard

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


There are 13 consecutive 8’s. Every other digit has a maximum span of 12.
unJon
unJon
  • Threads: 14
  • Posts: 4574
Joined: Jul 1, 2018
Thanked by
Ayecarumba
March 14th, 2019 at 3:01:32 PM permalink
Quote: Wizard

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



Some pi statistics here: https://bellard.org/pi/pi2700e9/pidigits.html

Shows thirteen 8s as the longest consecutive streak, starting at Pi digit 2164164669332.

Wasn’t there something about a string of zeros in Pi at the end of the Carl Sagan book Contact that the protagonist used to argue for the existence of a higher power?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Nathan
Nathan
  • Threads: 65
  • Posts: 3675
Joined: Sep 2, 2016
March 14th, 2019 at 3:58:47 PM permalink
All this math talk is making me heady. How about giving actual Pies some love? Lots of restaurants are selling pizza pies and normal pies for cheap! :D I got a .50 pizza slice today! Yum! :D
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D "Man Babes" #AxelFabulous "Olive oil is processed but it only has one ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D I sometimes speak in metaphors. ;) Remember this. ;) Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D "For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
Thanked by
mcallister3200
March 14th, 2019 at 4:17:29 PM permalink
Quote:

to those of you who don't like Nathan -- block her

so I did. Tell me I didn't click on this post anyway. But I did.

Noooooooooooooooooooooooo! When will I ever learn?
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
teliot
teliot
  • Threads: 43
  • Posts: 2871
Joined: Oct 19, 2009
March 14th, 2019 at 5:17:26 PM permalink
Quote: CrystalMath


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

Continued fraction convergents are an even faster method. But, I had not seen your method before ... curious.
Climate Casino: https://climatecasino.net/climate-casino/
teliot
teliot
  • Threads: 43
  • Posts: 2871
Joined: Oct 19, 2009
March 14th, 2019 at 5:20:46 PM permalink
2015 was the best PI day ever ... here is my proof, March 14, 2015 at 9:26:53.

Climate Casino: https://climatecasino.net/climate-casino/
teliot
teliot
  • Threads: 43
  • Posts: 2871
Joined: Oct 19, 2009
March 14th, 2019 at 5:24:19 PM permalink
Quote: Wizard

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.

"PI" is conjectured to be a normal number, which is a number that has all integers appearing somewhere in its decimal expansion according to its expected frequency. Aside from PI being transcendental, almost nothing is known about its decimal expansion.
Climate Casino: https://climatecasino.net/climate-casino/
gamerfreak
gamerfreak
  • Threads: 57
  • Posts: 3540
Joined: Dec 28, 2014
March 14th, 2019 at 5:26:06 PM permalink
Quote: gamerfreak

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


Some more interesting facts about this.

They used the Chudnovsky algorithm

And the current technological bottleneck to calculating more digits faster is not processor speed, but storage bandwidth:
http://www.numberworld.org/blogs/2019_3_14_pi_record/#major-difficulties
gamerfreak
gamerfreak
  • Threads: 57
  • Posts: 3540
Joined: Dec 28, 2014
March 14th, 2019 at 5:27:54 PM permalink
Quote: teliot

"PI" is conjectured to be a normal number, which is a number that has all integers appearing somewhere in its decimal expansion according to its expected frequency. Aside from PI being transcendental, almost nothing is known about its decimal expansion.


If it is a real number, how would we know if we reached the end when calculating a huge number of digits? Not sure if that question makes sense or not.
RS
RS
  • Threads: 62
  • Posts: 8626
Joined: Feb 11, 2014
March 14th, 2019 at 6:47:25 PM permalink
Quote: teliot

2015 was the best PI day ever ... here is my proof, March 14, 2015 at 9:26:53.


I applaud you for not rounding pi up to 3.141592654.
teliot
teliot
  • Threads: 43
  • Posts: 2871
Joined: Oct 19, 2009
March 14th, 2019 at 7:16:08 PM permalink
Quote: RS

Quote: teliot

2015 was the best PI day ever ... here is my proof, March 14, 2015 at 9:26:53.


I applaud you for not rounding pi up to 3.141592654.

Right, 4 is not the correct digit, and I was intent on 3 there. I was in front of my computer practicing "print screen" as the seconds at time.gov rolled by, until this fateful moment. I told a friend about this yesterday and his reply -- "oh, I could photoshop that ..."
Climate Casino: https://climatecasino.net/climate-casino/
onenickelmiracle
onenickelmiracle
  • Threads: 212
  • Posts: 8277
Joined: Jan 26, 2012
March 14th, 2019 at 7:57:35 PM permalink
I'll say it, I think Pi is different in every simulated universe, if they exist. There I go being crazy again because I watched a Youtube video once and before you. Duh, both are just guesses and for fun.
I am a robot.
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
March 15th, 2019 at 2:21:51 AM permalink
Quote: teliot

"PI" is conjectured to be a normal number, which is a number that has all integers appearing somewhere in its decimal expansion according to its expected frequency. Aside from PI being transcendental, almost nothing is known about its decimal expansion.

Is the following true? If they had found that after 100 decimal places, say, pi was all zeroes, that would mean it was not an irrational number after all?
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
unJon
unJon
  • Threads: 14
  • Posts: 4574
Joined: Jul 1, 2018
March 15th, 2019 at 2:25:52 AM permalink
Quote: odiousgambit

Is the following true? If they had found that after 100 decimal places, say, pi was all zeroes, that would mean it was not an irrational number after all?

Yes that would not be an irrational number.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
gordonm888
Administrator
gordonm888
  • Threads: 60
  • Posts: 5005
Joined: Feb 18, 2015
March 15th, 2019 at 8:46:45 AM permalink
Quote: CrystalMath


Happy pi day, and thanks, Miplet, for the table generator.



This is probably cheeky to ask, but I wonder if Miplet could modify his table generator so that the data entries are centered within the columns.

Its not enough to be good. Its also important to look good.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
miplet
miplet
  • Threads: 5
  • Posts: 2105
Joined: Dec 1, 2009
March 15th, 2019 at 10:06:27 AM permalink
Quote: gordonm888

This is probably cheeky to ask, but I wonder if Miplet could modify his table generator so that the data entries are centered within the columns.

Its not enough to be good. Its also important to look good.


He could and did. http://miplet.net/table/center.php .
“Man Babes” #AxelFabulous
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
March 15th, 2019 at 10:58:19 AM permalink
abc
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
DogHand
DogHand
  • Threads: 2
  • Posts: 1488
Joined: Sep 24, 2011
March 15th, 2019 at 12:14:03 PM permalink
gamerfreak,

Pi IS a real number, but because it is irrational, the decimal expansion of its digits never repeats. For a rational number (that is, a number that is the ratio of two integers), the digits eventually begin to repeat ad infinitum.

Hope this helps!

Dog Hand
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1909
Joined: May 10, 2011
March 15th, 2019 at 1:39:38 PM permalink
Quote: teliot

Continued fraction convergents are an even faster method. But, I had not seen your method before ... curious.



Messing around a bit today:
Discard the first 51 terms.
Calculate the next 51 terms and then apply the Pascal Triangle numbers, and I get pi to 46 places.
I heart Crystal Math.
TomG
TomG
  • Threads: 16
  • Posts: 2426
Joined: Sep 26, 2010
March 15th, 2019 at 4:04:21 PM permalink
One of the very first values for c/d used in human history was 3. So I vote to celebrate Pi for the entire month. The best pie in human history will always be cheesecake
gamerfreak
gamerfreak
  • Threads: 57
  • Posts: 3540
Joined: Dec 28, 2014
March 15th, 2019 at 4:55:20 PM permalink
Quote: DogHand

gamerfreak,

Pi IS a real number, but because it is irrational, the decimal expansion of its digits never repeats. For a rational number (that is, a number that is the ratio of two integers), the digits eventually begin to repeat ad infinitum.

Hope this helps!

Dog Hand


Yes, but how many repeating digits before you can be sure it’s the end of the number?

Like mentioned/linked previously, there are spans of 12/13 repeating digits.
sammydv
sammydv
  • Threads: 9
  • Posts: 624
Joined: Mar 25, 2016
March 16th, 2019 at 6:24:29 PM permalink
Quote: gamerfreak

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


Google ran like crap that day.
What google really did was have the worlds most resource intensive hogging AD for the google cloud service.
What a waste of the planets energy resources.
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
March 17th, 2019 at 2:11:27 AM permalink
Quote: TomG

One of the very first values for c/d used in human history was 3. So I vote to celebrate Pi for the entire month.

I still use "3" more often than any other pi number, in order to estimate the circumference of a tree [tho just as likely to use 1/pi, thus 1/3 , for an estimate of the diameter knowing the approx. circumf.]

It's a fallacy to think you are getting a more accurate number by taking pi out to more decimals if you are estimating diameter or circumference to begin with

at the moment I don't remember why I need that sometimes, though curiosity about a nice big tree is it often I think
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
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
March 17th, 2019 at 2:24:12 AM permalink
this got me wondering what people used in ancient times who needed more accuracy, they must have used 3 and one seventh

according to the calculator I usually use, this is an error of 0.0012644892673496615 in excess of actual pi
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
Joeman
Joeman
  • Threads: 36
  • Posts: 2410
Joined: Feb 21, 2014
March 17th, 2019 at 9:55:20 AM permalink
Hey, can we celebrate Pi Day all over again on the 22nd of July (22/7)?
"Dealer has 'rock'... Pay 'paper!'"
TomG
TomG
  • Threads: 16
  • Posts: 2426
Joined: Sep 26, 2010
March 17th, 2019 at 10:11:40 AM permalink
Quote: Joeman

Hey, can we celebrate Pi Day all over again on the 22nd of July (22/7)?



Absolutely. You can also celebrate it in January (3.1)
TomG
TomG
  • Threads: 16
  • Posts: 2426
Joined: Sep 26, 2010
March 17th, 2019 at 10:13:19 AM permalink
Quote: gamerfreak

Yes, but how many repeating digits before you can be sure it’s the end of the number?

Like mentioned/linked previously, there are spans of 12/13 repeating digits.



Use long division to solve 1 ÷ 3 and you'll see you can sometimes be sure after a number repeats one time
Lovecomps
Lovecomps
  • Threads: 79
  • Posts: 427
Joined: Aug 12, 2018
March 17th, 2019 at 1:40:39 PM permalink
FYI, pi isn't a number at all. It's a ratio.
The best things in life are not free.
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
March 17th, 2019 at 2:54:09 PM permalink
edited out something that made no sense

I went through a thing, during cocktail hour, but realize now that 3 and one seventh = 22/7

btw some more dead sea scrolls turned up, and there's some Genesis stuff in the new ones about pi that had been lost: 
Quote:

and then God said "Let the ratio of the circumference of a circle to its diameter equal about 22/7, but actually make it an irrational number, to drive certain types off the deep end"



PS you can diss 22/7 if you want to, but it represents less error than 3.14

error of 0.0015926535897932 [for 3.14] versus 0.0012644892673496 [for 22/7]
Last edited by: odiousgambit on Mar 17, 2019
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
miplet
miplet
  • Threads: 5
  • Posts: 2105
Joined: Dec 1, 2009
Thanked by
odiousgambit
March 17th, 2019 at 4:43:07 PM permalink
Quote: odiousgambit

edited out something that made no sense

I went through a thing, during cocktail hour, but realize now that 3 and one seventh = 22/7

btw some more dead sea scrolls turned up, and there's some Genesis stuff in the new ones about pi that had been lost: 


PS you can diss 22/7 if you want to, but it represents less error than 3.14

error of 0.0015926535897932 [for 3.14] versus 0.0012644892673496 [for 22/7]



http://turner.faculty.swau.edu/mathematics/materialslibrary/pi/pirat.html lists lots of fractions.
“Man Babes” #AxelFabulous
ssho88
ssho88
  • Threads: 53
  • Posts: 657
Joined: Oct 16, 2011
March 17th, 2019 at 9:14:54 PM permalink
Quote: CrystalMath

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.




What make you think that Pascal Triangle weighted method will give accurate answers ? Why don't just use simple average method?
odiousgambit
odiousgambit
  • Threads: 326
  • Posts: 9557
Joined: Nov 9, 2009
August 1st, 2019 at 5:27:37 PM permalink
Ordered pizza tonight, wanting a large, and the order desk said they had a special for two medium pizzas. So I asked which was actually more pizza, one large or two mediums? He indicated large was 14 inch and a medium 12 inch, but didn't know for sure what amounted to more. I knew they were circular pizzas of course.

Perhaps we both knew the formula for the area of a circle would give us the answer, but neither of us took a stab at it. I knew it could be deceiving, since the difference gets squared*. And the formula seemed daunting to try to do in my head, but I hadn't thought it out. So why shouldn't we have known after a just a moments thought?

The only thing that matters, to answer the question I asked, is the "radius squared" part, of course. 7^2 = 49, while 6^2 = 36, so two mediums would be 72, to exceed 49. The actual number of square inches is of no matter, so the actual value of pi*r^2 did not need to be crunched out as I initially assumed, not as far as the question is concerned.

*a 17 inch pizza would be approximately the same as two 12 inch mediums
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
FleaStiff
FleaStiff
  • Threads: 265
  • Posts: 14484
Joined: Oct 19, 2009
August 1st, 2019 at 5:42:48 PM permalink
WRONG.
Pizza is the dough, the cheese, the tomato, the anchovies or whatever and the girl in short shorts who delivers it.

Without knowing the quantity and quality differences it is impossible to answer.
ThatDonGuy
ThatDonGuy
  • Threads: 117
  • Posts: 6219
Joined: Jun 22, 2011
Thanked by
odiousgambit
August 1st, 2019 at 6:00:20 PM permalink
Quote: odiousgambit

Ordered pizza tonight, wanting a large, and the order desk said they had a special for two medium pizzas. So I asked which was actually more pizza, one large or two mediums? He indicated large was 14 inch and a medium 12 inch, but didn't know for sure what amounted to more. I knew they were circular pizzas of course.

Perhaps we both knew the formula for the area of a circle would give us the answer, but neither of us took a stab at it. I knew it could be deceiving, since the difference gets squared*. And the formula seemed daunting to try to do in my head, but I hadn't thought it out. So why shouldn't we have known after a just a moments thought?

The only thing that matters, to answer the question I asked, is the "radius squared" part, of course. 7^2 = 49, while 6^2 = 36, so two mediums would be 72, to exceed 49. The actual number of square inches is of no matter, so the actual value of pi*r^2 did not need to be crunched out as I initially assumed, not as far as the question is concerned.

*a 17 inch pizza would be approximately the same as two 12 inch mediums


Well, maybe not easier in your specific case, as both diameters were even numbers, but you can also use the diameter squared, since area = diameter squared x (PI / 4).

And when did medium / large / XL drop from 14 / 16 / 18 inches to 12 / 14 / 16? Round Table caught me off guard with this.
Ace2
Ace2
  • Threads: 32
  • Posts: 2672
Joined: Oct 2, 2017
Thanked by
odiousgambit
August 1st, 2019 at 8:47:26 PM permalink
Two 12s definitely sounds like more than one 14 without doing any calculation.

Two 10s wouldn’t be so definite without a calc. And even though the large is slightly less at 49pi, I go with that. Only 1 pi less area, but 30% less crust.

If you ever need a shortcut while ordering a pizza, remember the square root of 2 is 1.41. So if the large /medium ratio is above 2^.5, go with large assuming area is the only deciding factor. Otherwise get 2 medium
It’s all about making that GTA
onenickelmiracle
onenickelmiracle
  • Threads: 212
  • Posts: 8277
Joined: Jan 26, 2012
August 1st, 2019 at 11:16:45 PM permalink
I'd have to know the size of the crust. I kind of think both will have outer crusts the same size, so probably looking at a 13" and two 11"s. I devalue the crust. It's 2:16 now oh, that's as far as this post wants to go.
I am a robot.
billryan
billryan
  • Threads: 240
  • Posts: 16282
Joined: Nov 2, 2009
August 2nd, 2019 at 10:22:37 AM permalink
Quote: TomG

One of the very first values for c/d used in human history was 3. So I vote to celebrate Pi for the entire month. The best pie in human history will always be cheesecake



Pizza pie!
The difference between fiction and reality is that fiction is supposed to make sense.
billryan
billryan
  • Threads: 240
  • Posts: 16282
Joined: Nov 2, 2009
August 2nd, 2019 at 10:25:40 AM permalink
Quote: ThatDonGuy

Quote: odiousgambit

Ordered pizza tonight, wanting a large, and the order desk said they had a special for two medium pizzas. So I asked which was actually more pizza, one large or two mediums? He indicated large was 14 inch and a medium 12 inch, but didn't know for sure what amounted to more. I knew they were circular pizzas of course.

Perhaps we both knew the formula for the area of a circle would give us the answer, but neither of us took a stab at it. I knew it could be deceiving, since the difference gets squared*. And the formula seemed daunting to try to do in my head, but I hadn't thought it out. So why shouldn't we have known after a just a moments thought?

The only thing that matters, to answer the question I asked, is the "radius squared" part, of course. 7^2 = 49, while 6^2 = 36, so two mediums would be 72, to exceed 49. The actual number of square inches is of no matter, so the actual value of pi*r^2 did not need to be crunched out as I initially assumed, not as far as the question is concerned.

*a 17 inch pizza would be approximately the same as two 12 inch mediums


Well, maybe not easier in your specific case, as both diameters were even numbers, but you can also use the diameter squared, since area = diameter squared x (PI / 4).

And when did medium / large / XL drop from 14 / 16 / 18 inches to 12 / 14 / 16? Round Table caught me off guard with this.



Its stupid, but it still bothers me that you can get as many slices from a small pie than from a large one. I think pies under 12 inches should only have 4 slices. Order a XXXL pie and it should be 10-12 slices.
The difference between fiction and reality is that fiction is supposed to make sense.
Ace2
Ace2
  • Threads: 32
  • Posts: 2672
Joined: Oct 2, 2017
August 2nd, 2019 at 10:26:52 AM permalink
I can think of a much better pie than that.
It’s all about making that GTA
Ayecarumba
Ayecarumba
  • Threads: 236
  • Posts: 6763
Joined: Nov 17, 2009
Thanked by
Ace2
August 2nd, 2019 at 11:22:09 AM permalink
Quote: Ace2

I can think of a much better pie than that.



Banana Cream?
Simplicity is the ultimate sophistication - Leonardo da Vinci
  • Jump to: