Happy pi day!

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)?

Quote: Wizard

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

Quote: Wizard

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

Quote:

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

Quote: CrystalMath

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

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.

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

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.

Quote: teliot

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

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.

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.

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?

Quote: CrystalMath

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

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.

Quote: teliot

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

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

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

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.

Quote: Joeman

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

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.

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"

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]

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 Number	Term	Cumulative Value	Multiplier	Contribution to pi/4
0	+1/1	1	1	8.88178E-16
1	-1/3	0.666666667	50	2.96059E-14
2	+1/5	0.866666667	1,225	9.42949E-13
3	-1/7	0.723809524	19,600	1.26003E-11
4	+1/9	0.834920635	230,300	1.70781E-10
5	-1/11	0.744011544	2,118,760	1.40011E-09
6	+1/13	0.820934621	15,890,700	1.15865E-08
7	-1/15	0.754267954	99,884,400	6.6915E-08
8	+1/17	0.813091484	536,878,650	3.87718E-07
9	-1/19	0.760459905	2,505,433,700	1.69223E-06
10	+1/21	0.808078952	10,272,278,170	7.3726E-06
11	-1/23	0.764600691	37,353,738,800	2.5367E-05
12	+1/25	0.804600691	121,399,651,100	8.67557E-05
13	-1/27	0.767563654	354,860,518,600	0.00024192
14	+1/29	0.802046413	937,845,656,300	0.000668084
15	-1/31	0.769788349	2,250,829,575,120	0.001538913
16	+1/33	0.800091379	4,923,689,695,575	0.003498892
17	-1/35	0.77151995	9,847,379,391,150	0.006747891
18	+1/37	0.798546977	18,053,528,883,775	0.012804505
19	-1/39	0.772905952	30,405,943,383,200	0.020873023
20	+1/41	0.797296196	47,129,212,243,960	0.03337414
21	-1/43	0.774040382	67,327,446,062,800	0.046286674
22	+1/45	0.796262604	88,749,815,264,600	0.062765934
23	-1/47	0.774986008	108,043,253,365,600	0.074368964
24	+1/49	0.795394171	121,548,660,036,300	0.085868286
25	-1/51	0.775786328	126,410,606,437,752	0.087101544
26	+1/53	0.794654253	121,548,660,036,300	0.085788407
27	-1/55	0.776472435	108,043,253,365,600	0.074511604
28	+1/57	0.794016294	88,749,815,264,600	0.062588867
29	-1/59	0.777067142	67,327,446,062,800	0.046467671
30	+1/61	0.793460584	47,129,212,243,960	0.033213585
31	-1/63	0.777587568	30,405,943,383,200	0.020999454
32	+1/65	0.792972184	18,053,528,883,775	0.012715114
33	-1/67	0.778046811	9,847,379,391,150	0.006804976
34	+1/69	0.792539564	4,923,689,695,575	0.003465867
35	-1/71	0.778455057	2,250,829,575,120	0.001556239
36	+1/73	0.792153687	937,845,656,300	0.000659844
37	-1/75	0.778820354	354,860,518,600	0.000245468
38	+1/77	0.791807367	121,399,651,100	8.53763E-05
39	-1/79	0.779149139	37,353,738,800	2.58497E-05
40	+1/81	0.791494818	10,272,278,170	7.22129E-06
41	-1/83	0.779446625	2,505,433,700	1.73448E-06
42	+1/85	0.791211331	536,878,650	3.77284E-07
43	-1/87	0.779717078	99,884,400	6.91727E-08
44	+1/89	0.790953034	15,890,700	1.11633E-08
45	-1/91	0.779964023	2,118,760	1.46777E-09
46	+1/93	0.790716711	230,300	1.61739E-10
47	-1/95	0.780190395	19,600	1.35818E-11
48	+1/97	0.790499673	1,225	8.60078E-13
49	-1/99	0.780398663	50	3.46567E-14
50	+1/101	0.790299653	1	7.01927E-16
Total			1,125,899,906,842,620	0.78539816339744900

Value	Number
pi/4 estimate	0.78539816339744900
pi estimate	3.14159265358979000
pi() - excel function	3.14159265358979000

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.

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?

giving the answer now since this is too easy

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

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

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?

giving the answer now since this is too easy

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

You could have made it easier

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.

Quote: Ace2

I can think of a much better pie than that.