Dear Bill - I agree with you 100% that the Greek letter *tau *should honor Gamma(1/4) = 3.625... (though I confess to having a fondness for *tau*^4, maybe because it's easier -- for me -- to remember that it's near 173). Should some enlightened individuals start a campaign to celebrate a true *Tau Day *in honor of Gamma(1/4)? (2π and June 28 are OK, but NOT *tau* = 2π -- c'mon people, seriously, grow up -- there's no need to throw away another Greek letter, 'cause they ain't making any new ones!) But when to kick off the new, true Tau Day?? Perhaps on 3/6/25, which could mean either March 6, 2025 or 3 June 2025 depending on where you are located? That would give two different target dates to aim for, in case only 3.6... people show up for the party on March 6. Or should it be 10 days after Star Wars Day, with the slogan "May One-Four ^th Be With You"? *Or, perhaps the funniest idea so far, should the annual celebrations commence in Israel, in conjunction with 1 April, since "Gam ma 1/4" means "Also from April 1" *(Heb./Eng. translation: G.Huber)*.* This latter possibility could help to alleviate the worries of those stereotypical Jewish parents who spent undue time and effort sending their kids money in foreign currency, all because of some joker named Rothberg, according to "The Schmooze" section of *The Forward:* https://forward.com/schmooze/154158/israeli-april-fools-jokes-went-too-far/ . Instead, those anxious parents would know that on April Fools' Day their children are studying the properties of the Gamma function, not to mention the many shekels said parents and kids would save because Artin's book is available as a Dover reprint. Furthermore, to the list of leg-pulling utterances such as "I saw your car being towed" and "A beautiful lady asked me to give this phone number to you" (both suggested here https://www.hebrewpod101.com/blog/2018/03/19/how-to-celebrate-april-fools-da... ) one could add remarks especially designed for a dual-purpose April-Fools'/Tau-Day, such as: "I saw your keys around the first zero of the Gamma function" (oh boy! imagine the belly laughs while the remarkee looks around for that), or "Let's do a Zoom call around Gamma of 0 'clock" (they wait centuries in the Zoom room, as you barely suppress guffaws) So, Bill, it seems a true *tau*-inspired Tau Day would truly be a multifaceted laughfest, whenever it happens to happen. -- Greg. ==================== G Huber Theory, Biohub San Francisco, CA On Wed, Dec 16, 2020 at 2:22 AM Bill Gosper <billgosper@gmail.com> wrote:
The arclength of one period of sin x = the circumference of an ellipse with semiaxes 1 and √2.
In[112]:= #1 == #2 == FunctionExpand@#1== N@# &[ArcLength[Circle[{0, 0}, {√2, 1}]], ArcLength[Sin@x, {x, 0, 2 π]}]]
Out[112]= 4 EllipticE[-1] == 4 √2 EllipticE[1/2] == 4 √2 π^(3/2)/Gamma[1/4]^2 + Gamma[1/4]^2/√(2π) == 7.64039557805542
𝚪(¼) is the rightful value of the symbol 𝛕. And someone should write Beckmann II: A History of 𝛕. —rwg