Hank Posted March 15, 2021 Report Share Posted March 15, 2021 1 minute ago, EricJ said: EVERY day is a good day for pie! 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 15, 2021 Author Report Share Posted March 15, 2021 15 minutes ago, EricJ said: Nobody ever says anything about e on February 7. Well - perhaps we can have an e-day on Feb 2. and a sqrt(5) day on Feb 23. And a sqrt(17) day on April 12. Unfortunately soon they will combine those dates and call it numbers day. Which will be April 15 - and on numbers day they will ask all Americans to compute lots of numbers and send money to the federal government. Big numbers. The best numbers. 2 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 15, 2021 Author Report Share Posted March 15, 2021 23 minutes ago, Hank said: This would be more impressive if you calculated by hand and showed your work. Using a computer is cheatin!! Not lil' ol' ME! By the way the next digit after the 20,000th digit is an 8. Quote Link to comment Share on other sites More sharing options...
bradp Posted March 17, 2021 Report Share Posted March 17, 2021 From the interwebs: 1 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 17, 2021 Author Report Share Posted March 17, 2021 6 minutes ago, bradp said: From the interwebs: That is a really beautiful graphic! Thank you. I am adding it to my collection of cool math demos for classroom use someday. This is related to a long running question called the normality of pi. Regarding how are the digits distributed. Is it a uniform distribution? And the more advanced version, which is if I compute pi but in base D, then what is the distribution of digits? Uniform? (Base D as in we work in base 10 but that is an accident of evolution and not a deep thing of the nature of mathematics - what if human kind had 6 digits per hand - or 4 digits like Disney cartoons - then we would likey be working usually in base D=12 or 8 respectively - computers like base D=2). Here is a discussion https://ui.adsabs.harvard.edu/abs/2005IJMPC..16..281T/abstract http://interstat.statjournals.net/YEAR/2006/articles/0601001.pdf Quote Link to comment Share on other sites More sharing options...
bradp Posted March 17, 2021 Report Share Posted March 17, 2021 That’s really interesting Erik. Also this is probably my favorite graphic from the internet I've seen in a long time. It’s so simple but very beautiful as it progresses and you kind of sit there like a movie staring at it winding what’s going to happen next. Quote Link to comment Share on other sites More sharing options...
Hank Posted March 17, 2021 Report Share Posted March 17, 2021 3 minutes ago, aviatoreb said: That is a really beautiful graphic! Thank you. I am adding it to my collection of cool math demos for classroom use someday. This is related to a long running question called the normality of pi. Regarding how are the digits distributed. Is it a uniform distribution? And the more advanced version, which is if I compute pi but in base D, then what is the distribution of digits? Uniform? (Base D as in we work in base 10 but that is an accident of evolution and not a deep thing of the nature of mathematics - what if human kind had 6 digits per hand - or 4 digits like Disney cartoons - then we would likey be working usually in base D=12 or 8 respectively - computers like base D=2). Here is a discussion https://ui.adsabs.harvard.edu/abs/2005IJMPC..16..281T/abstract http://interstat.statjournals.net/YEAR/2006/articles/0601001.pdf Some cultures in the Ancient Near East used Base 60, counting with each joint in their fingers. That's how we ended up with 60 minutes in an hour, 360° in a circle, etc. But you probably know this . . . . 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 17, 2021 Author Report Share Posted March 17, 2021 47 minutes ago, Hank said: Some cultures in the Ancient Near East used Base 60, counting with each joint in their fingers. That's how we ended up with 60 minutes in an hour, 360° in a circle, etc. But you probably know this . . . . Four Score and Seven Years ago Today.... Quote Link to comment Share on other sites More sharing options...
Hank Posted March 17, 2021 Report Share Posted March 17, 2021 1 hour ago, aviatoreb said: Four Score and Seven Years ago Today.... A Physics instructor once said that all units of measure are arbitrary and chosen by custom. There's nothing special about any particular scheme or unit. His favorite example was measuring speed in furlongs per fortnight . . . . Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 17, 2021 Author Report Share Posted March 17, 2021 54 minutes ago, Hank said: A Physics instructor once said that all units of measure are arbitrary and chosen by custom. There's nothing special about any particular scheme or unit. His favorite example was measuring speed in furlongs per fortnight . . . . Right - I think you and I have also discussed this very unit - furlongs per fortnight. Since it is one of my favorites too. I remember as a student spending a semester in England at Warwick University and I decided to row on the crew team for the period as I rowed back home - and they wanted to know how much I weight - in stone. How many stone do you weigh? Rowing on the Avon - of Shakespeare fame. I feel that base 10 is sentimentally highly relevant for humans since out ten digits on our hands. But 20 our 20 digits on hands and feet. However no deep mathematical significance. Base 2 for computers. Base e for calculus (and this pesky chain rule). Its hard to convince me anything else has any real relevance beyond an accident of biology or history. Quote Link to comment Share on other sites More sharing options...
EricJ Posted March 17, 2021 Report Share Posted March 17, 2021 (edited) 8 hours ago, aviatoreb said: That is a really beautiful graphic! Thank you. I am adding it to my collection of cool math demos for classroom use someday. This is related to a long running question called the normality of pi. Regarding how are the digits distributed. Is it a uniform distribution? And the more advanced version, which is if I compute pi but in base D, then what is the distribution of digits? Uniform? (Base D as in we work in base 10 but that is an accident of evolution and not a deep thing of the nature of mathematics - what if human kind had 6 digits per hand - or 4 digits like Disney cartoons - then we would likey be working usually in base D=12 or 8 respectively - computers like base D=2). Here is a discussion https://ui.adsabs.harvard.edu/abs/2005IJMPC..16..281T/abstract http://interstat.statjournals.net/YEAR/2006/articles/0601001.pdf In hexadecimal there is a closed-form solution to compute any arbitrary-precision digit in Pi without knowing the previous digits. This is only known to work in hexadecimal. There may be proofs that it isn't possible in some bases, I don't recall the details.https://giordano.github.io/blog/2017-11-21-hexadecimal-pi/ Edited March 17, 2021 by EricJ Quote Link to comment Share on other sites More sharing options...
ArtVandelay Posted March 17, 2021 Report Share Posted March 17, 2021 How Newton changed how we calculated Pi. 2 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 17, 2021 Author Report Share Posted March 17, 2021 2 hours ago, EricJ said: In hexadecimal there is a closed-form solution to compute any arbitrary-precision digit in Pi without knowing the previous digits. This is only known to work in hexadecimal. There may be proofs that it isn't possible in some bases, I don't recall the details.https://giordano.github.io/blog/2017-11-21-hexadecimal-pi/ Right - that's the BPP formula which is a so-called spigot formula as it can produce the nth digit directly without bothering to compute all the digits before - which is surprising! But nonetheless not efficient. It was central in discussion of the normality of pi. I had a memory - but I cannot confirm it now so I might be wrong..that there was a BPP formula for other base arithmetic besides hex. https://www.davidhbailey.com/dhbpapers/normality-digits-pi.pdf. see Eq 3 page 6. https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula same guys also wrote this terrific review article. https://www.ams.org/notices/201307/rnoti-p844.pdf Quote Link to comment Share on other sites More sharing options...
EricJ Posted March 17, 2021 Report Share Posted March 17, 2021 26 minutes ago, aviatoreb said: I had a memory - but I cannot confirm it now so I might be wrong..that there was a BPP formula for other base arithmetic besides hex. https://www.davidhbailey.com/dhbpapers/normality-digits-pi.pdf. see Eq 3 page 6. https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula They say in the linked references that it also works for binary, but it appears that's just an extension of it being hexadecimal. That may imply that it works in base 4 as well. I'm too lazy to look close enough to sort it out myself. 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 18, 2021 Author Report Share Posted March 18, 2021 42 minutes ago, EricJ said: They say in the linked references that it also works for binary, but it appears that's just an extension of it being hexadecimal. That may imply that it works in base 4 as well. I'm too lazy to look close enough to sort it out myself. I think you are right. I had by folklore been under the impression there was a more general formula but now I am doubting it. Its Eq 6 that caught my eye a number of years ago when it first came out (actually I saw him give a talk at a conference and immediately download the paper). This is a connection between the question of normality to a dynamical system, Eq 6 and questions of its ergodicity. I don't actually normally (pun) work in pure math questions like the normality of pi but I was delighted to see it reduce to a question of dynamical system that I normally just work in more applied settings. 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 14, 2022 Author Report Share Posted March 14, 2022 Reviving an old thread - on its anniversary - yet again today is Pi Day. Happy round things friends. Careful scrolling since I hear that the 3,141 digits of Pi I posted a few years ago are slow loading. Here's my pi-plane getting topped off this am. 3 Quote Link to comment Share on other sites More sharing options...
ohdub Posted March 14, 2022 Report Share Posted March 14, 2022 Happy Pi Day @aviatoreb! 2 Quote Link to comment Share on other sites More sharing options...
carusoam Posted March 15, 2022 Report Share Posted March 15, 2022 Merry pi day, a day late… There are so many round things and things that turn around constantly in our planes… I remember pi day and Erik’s pi plane every year… I almost forgot about the extra long version, pages of pi, that got posted…. That probably took me 3.14 days to get to the bottom of that post so I could say I read every post in that thread… Best regards, -a- 2 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 15, 2022 Author Report Share Posted March 15, 2022 Thank you all! Did I mention that Pi is my second favorite number? Oh for that long posting of digits of Pi - funny it takes so long to load. I can compute a million digits of Pi in about a fraction of a second with the command N[Pi, 1000000] entered into an implementation of Mathematica on this computer. Quote Link to comment Share on other sites More sharing options...
rbp Posted March 16, 2022 Report Share Posted March 16, 2022 The real pi day is july 22 1 Quote Link to comment Share on other sites More sharing options...
Hank Posted March 16, 2022 Report Share Posted March 16, 2022 (edited) Sadly, I was a day late on the celebration. I remembered Pi Day yesterday, and had a wood-fired Cajun Shrimp & Sausage pizza for supper tonight. If only the restaurant had good beer . . . . Edited March 16, 2022 by Hank Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 16, 2022 Author Report Share Posted March 16, 2022 10 minutes ago, Hank said: Sadly, I was a day late on the celebration. I remembered Pi Day yesterday, and had a wood-fired Cajun Shrimp & Sausage pizza for supper tonight. If only the restaurant had good beer . . . . Or / maybe your a 364 days early! 1 Quote Link to comment Share on other sites More sharing options...
EricJ Posted March 16, 2022 Report Share Posted March 16, 2022 20 hours ago, rbp said: The real pi day is july 22 For approximately rational people. 2 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 16, 2022 Author Report Share Posted March 16, 2022 29 minutes ago, EricJ said: For approximately rational people. However, since the rational numbers are dense in the set of real numbers that equals the set of rationals union the set of irrationals, then it follows that all approximately rational people in fact include all the irrational people. 2 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted March 16, 2022 Author Report Share Posted March 16, 2022 21 hours ago, rbp said: The real pi day is july 22 Now that's just plane crazy talk. Quote Link to comment Share on other sites More sharing options...
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