tag:blogger.com,1999:blog-3722233.post1553698753003694648..comments2024-05-26T22:10:45.398-05:00Comments on Computational Complexity: Archimedes, Pi, and PickelballLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3722233.post-1340495971853897222023-12-22T19:57:00.040-06:002023-12-22T19:57:00.040-06:00(Bill) Georgios and Mike - Excellent points! It ha...(Bill) Georgios and Mike - Excellent points! It had no dawned on me that in Greece they WOULD call it Archimedias Constant (or close to that). And I had not through of rigously testing the hypothesis that it was really not used (on Google books, which is mostly English). Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-9394576678030892212023-12-22T16:45:57.829-06:002023-12-22T16:45:57.829-06:00When I look in Google Books Ngram nothing shows up...When I look in Google Books Ngram nothing shows up for Archimedes constant (with or without hyphen, plural or possessive)<br />before 1966. For Archimedes number it is 1940.Mike Smithnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-72175881475997197772023-12-21T07:04:55.650-06:002023-12-21T07:04:55.650-06:00Hi Bill, Lance,
I am Greek and in my Greek school ...Hi Bill, Lance,<br />I am Greek and in my Greek school years (30 years ago) π was introduced to us as "Aρχιμήδεια Σταθερά" (Archimedean Constant) by our math teacher. Georgios Stamoulisnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-55518575114185668002023-12-18T08:25:06.605-06:002023-12-18T08:25:06.605-06:00Even that is behind a paywall. I found the article...Even that is behind a paywall. I found the article on ArXiv: <a href="https://arxiv.org/abs/1303.0904" rel="nofollow">https://arxiv.org/abs/1303.0904</a>.Lance Fortnowhttps://www.blogger.com/profile/06752030912874378610noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-54123224203200104812023-12-18T08:18:06.577-06:002023-12-18T08:18:06.577-06:00(bill) If you want to use math in a comment do the...(bill) If you want to use math in a comment do the following: <br />slash \ <br />open parenthesis (<br />math you want, for example slash then pi. DO NOT use dollar signs<br />slash \<br />closed parenthesis ) Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-63572389538812758192023-12-18T08:15:04.263-06:002023-12-18T08:15:04.263-06:00(bill test) Wondering if commenters can use math. ...(bill test) Wondering if commenters can use math. So I am trying it. PI is \(\pi\)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-15003399118799329832023-12-18T08:06:18.681-06:002023-12-18T08:06:18.681-06:00Oops. This is probably a better link. https://doi....Oops. This is probably a better link. https://doi.org/10.4169/college.math.j.46.3.162David Richesonhttp://divisbyzero.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-45978022553615811732023-12-18T08:01:27.829-06:002023-12-18T08:01:27.829-06:00I have read similar things about people calling it...I have read similar things about people calling it Archimedes's number. I wonder if this is similar to the lazy journalism of "It has been said that..." when in fact the only people saying it are people saying that people are saying it.<br /><br />I will confess, that the last sentence of my 2015 article "Circular Reasoning: Who First Proved That C Divided by d Is a Constant?" (https://www-tandfonline-com.dickinson.idm.oclc.org/doi/abs/10.4169/college.math.j.46.3.162) is "Because of these results about the nature of π and his very accurate bounds on the value, it seems fitting that we call π Archimedes’s number." David Richesonhttps://divisbyzero.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24284578932785649562023-12-18T02:26:57.764-06:002023-12-18T02:26:57.764-06:00While there might be a unanimous vote of confidenc...While there might be a unanimous vote of confidence amongst<br />mathematicians that Archimedes represents a great constant <br />in the history of geometry (i.e., one of our revered friends christened a yacht after him), the history behind the origin of the letter or symbol $\pi$ and its correct attribution with respect to the ratio of circumference to diameter, remains a bit less unanimously clear -- perhaps even a bit nebulous.<br /><br />We know that there were other people, such as William Oughtred <br />and Isaac Barrow, who associated the letter $\pi$ as a<br />variable relating to the circle -- predating our Welsh friend William Jones. <br />Further, while we do know William Jones. While we do know William Jones used $\pi$ to denote our `constant', he used it to describe work by "The Truly Ingenious John Machin." <br />This organically leads to the question: <br />should it be attributed to the man whose work he actually endorsed or cited?<br /><br />A probably more interesting (not necessarily better) question would <br />be: whose stamp of approval was necessary to popularize $\pi$ and<br />standardize it? Some might argue that it wasn't until Euler adopted it,<br />and used it as early as 1736 in "Mechanica, sive, Motus scientia analytice exposita" in<br />Volume I, on page 123 under "Proposito 38, Theorema 304.":<br />".... et $\pi$ : 1 rationem peripheriae ad diametrum." -- translating from Latin to English as "and $\pi$ : 1 ratio of the periphery to the diameter."<br /><br />In Volume II, on page 70: "et ratio perifpheriae ad diametrum = \pi" which translates from Latin to English <br />as "and the ratio of the periphery to the diameter = \pi."<br />(NB: `perifpheriae' should have been `peripheriae' or `periferiae', but here we witness a typographical mistake in Latin.)<br /><br />Interestingly, before Euler adopted using $\pi,$ he kept using symbols, p and c. John Bernoulli used to employ the Latin letter, c. So, presumably Euler first converged to Bernoulli's notation, i.e., from p to c, before finally popularizing a new <br />standard and declaring it to be $\pi.$Evangelos Georgiadisnoreply@blogger.com