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State of the Tau 2024

It’s that time of year again: the summer (or winter!) solstice, high school graduations, college commencements, and of course Tau Day!

Michael Hartl here, founder of Tau Day and author of The Tau Manifesto. Thanks for joining me for another year of celebrating the true circle constant—the ratio of a circle’s circumference, not to its diameter, but to its radius:

\[ \tau = \frac{C}{r} = 6.283185\ldots \]

First publicly proposed in 2010 by The Tau Manifesto (now available both online and as a print edition at Amazon), tau has seen adoption by thousands (millions?) of math enthusiasts around the world, including the official Google calculator, the Python programming language, and (new this year!) iOS, Apple’s ubiquitous mobile operating system.

The State of the Tau 2024 is published jointly on the Tau Day website, on Substack, and on my personal website. In addition to tau topics, my posts chronicle my current math learning project, including lots of recommendations for math learning resources. Subscribe to my Substack for free post notifications, join as a paid subscriber to support my work financially, or join as a Founding Member to get a personal video chat with me on any subject of your choosing!

Without further ado, here are some highlights from the world of tau since Tau Day last year:

SLMath 2024

Last December, I had the pleasure of visiting the Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) for the second time. And for the first time, I had a chance to meet SLMath’s accomplished director, Dr. Tatiana Toro, who is also a professor of mathematics at the University of Washington. Thanks so much to Tatiana and to SLMath Assistant Director Uta Lorenzen for being such gracious hosts during my visit.

Michael Hartl and Tatiana Toro

For Tau Day this year, SLMath is outdoing their already impressive efforts the past two years by running a fundraiser and not one but two puzzle contests. The first puzzle is a crossword created by former SLMath postdoc Melissa Zhang, with a top prize that includes an Official Tau Shirt. The second is a challenging puzzle called “The Blob”, created by puzzle master Peter Winkler of Dartmouth College. Check them both out on the SLMath Tau Day Page!

As part of the Tau Day celebrations, you can donate to SLMath, with double the impact of your gift thanks to generous matching donations. SLMath is one of the most highly regarded mathematical research institutions in the world, so please join me in supporting this remarkable organization!

Computers and programming languages

Since Tau Day 2023, I found out that the Nim systems programming language includes tau, as does the Manim math animation library (originally developed by the great 3Blue1Brown and used by sudgylacmoe to make the animated version of The Tau Manifesto last year). These resources join languages like Microsoft .NET, Rust, Java, and Python in supporting tau—quite a collection!

Perhaps the most exciting development in the past year is the inclusion of tau when converting degrees in iOS, the operating system of Apple’s iPhone. If you have such a device, you can confirm this one yourself using the Messages app: send a text to a friend with some number of degrees (symbolically or in words, as in “90°” or “90 degrees”) and then click on the “degrees” part of the message. You’ll be given the option to convert the angle to “Turns” in terms of $\tau$!

Converting angles to turns in iOS

When I shared this remarkable turn (heh) of events with original “Pi Is Wrong!” author Bob Palais, he noted that tau (which I sometimes refer to as a “social hack”) has now gone out to billions of people—or, using the metric prefix giga-, meaning “billion”—out to gigapeople:

I’d say when you’ve reached the level of “gigapeople”, your social hack can by now be deemed to have conquered the world! 😊

As always, thanks to Bob (whom I like to think of as the “Godfather of Tau”) for his continued support!

Twitter roundup 2024

As with every year since the original publication of The Tau Manifesto, the last year saw lots of tau-related activity on Twitter (or should I say 𝕏? No, I don’t think I will.).

MIT (again)

MIT once again voiced its support for Tau Day, which is much appreciated coming from one of the top two tech schools in America. (The other one—Caltech, which is my own graduate school alma mater—really needs to get on the ball on this one!)

Elon Musk (again)

Known tau supporter (and Tau Day birthday boy) Elon Musk revealed that his son Tau Techno Mechanicus was named after the true circle constant. (In the tweet below, Elon surely meant to say Circumference/Radius, not Circumference/Diameter—the damage wrought by pi runs deep, and we clearly still have much work to do.)

Thanks for the support, Elon—and happy birthday! (I’m still going to keep calling it “Twitter”, though.)

Vitalik Buterin (again)

Another known tau supporter, Ethereum cofounder Vitalik Buterin, once again offered Tau Day his support. Thanks, Vitalik!

David Chapman and Meaningness

I was especially pleased to discover that David Chapman, a.k.a. @Meaningness, celebrates Tau Day. I first discovered Chapman’s remarkable hypertext book Meaningness around five years ago and found it endlessly fascinating. Meaningness is a profound meditation on meaning and purpose and I recommend it highly. It was a real thrill to discover that the author of such a remarkable work is also a fan of tau.

Comic relief

A little comic relief came from Twitter account @AxiometricGames via the They Don’t Know meme. Once you’ve seen the light and converted to tauism, it can seem a little lonely on Pi Day (a.k.a. Half Tau Day), but I suggest joining in the fun—and maybe, very gently, broaching the subject of tau (but only if you’re sure the other person is receptive).

Miscellany

Finally, I’ve got a couple of miscellaneous loose ends to share. The first is a video about, of all things, the effects of a cast saw on human skin. In the sponsorship section (which is for a shaving company), the video host describes a 30° angle as “tau on twelve radians”, letting the viewer infer what exactly that must mean. This is just the kind of casual usage that reinforces tau as a natural constant that anyone can understand.

The second loose end is a wonderful Vi Hart video I somehow missed from way back in 2013 (discovered via this tweet). Please enjoy Vi’s delightful song about tau!


State of the Tau 2023

Hey Google, when is Tau Day this year?

The result of a Google search for 'tau day'

Ah, yes—that’s today. Happy Tau Day, everyone!

I’m Michael Hartl, founder of Tau Day and author of The Tau Manifesto. Thanks for joining me in the celebration of the true circle constant, tau:

\[ \tau = \frac{C}{r} = 6.283185\ldots \]

As in previous years, I’ve made minor updates to The Tau Manifesto, Tau Day’s (and tau’s) founding document, which is available both online and as a print edition at Amazon. And as always, you can show your support for tau by wearing an Official Tau Shirt. You can even follow along with and share the day’s activities in real time using the #TauDay hashtag on Twitter.

Finally, I’m pleased to announce that I’ve started Michael Hartl’s Substack, a newsletter and blog that includes tau-related announcements (such as this one). As part of this, I’ve moved the main tau mailing list over from my old email software to Substack. As with any Substack, you can unsubscribe at any time using the link at the bottom of each message.

My Substack has both free and paid tiers, and my plan is to include tau-related news among the free posts. My plan for paid posts is to focus (at least initially) on math and math learning, including curated book and YouTube recommendations, as well as details about my current personal project to learn pure mathematics. (Clearly, I must know at least some math, but I’m planning to learn more. How much more, and why? Subscribe to find out!)

Without further ado, here are some of the highlights in the world of tau since Tau Day last year:

Read on for more details about these happenings. Enjoy!

The Tau Manifesto, animated version

Sometime early in 2022, I found the great video A Swift Introduction to Geometric Algebra by math YouTuber sudgylacmoe. It was created using Manim, an open-source version of the animation software developed for the wildly popular 3Blue1Brown YouTube channel, and introduces the remarkable field of geometric (Clifford) algebra.

I thought sudgy’s video was fantastic, and I also happened to notice a delightful detail: it uses tau!

The use of tau in A Swift Introduction to Geometric Algebra

One of my favorite things about the video is that it doesn’t even bother introducing tau—it just goes ahead uses it, secure in the knowledge that viewers either already know about it or can figure it out from context.

I thought this use of tau was so cool, and enjoyed the video so much, that I actually tried to track down sudgy’s email address so I could reach out to him directly. Unfortunately, I was unsuccessful in this attempt, but fortunately sudgy himself emailed me on Tau Day last year!

Among other things, sudgy proposed collaborating on an animated version of The Tau Manifesto, which I thought was a great idea. The result, which just launched for Tau Day 2023, is available here:


The script for the video was adapted from the text of The Tau Manifesto, with both me and sudgy narrating, and the amazing animation is all sudgy. Thanks to sudgy for the enjoyable collaboration and for all the great work!

Java and Liberty Eiffel

Java and Liberty Eiffel have joined languages such as Microsoft .NET, Rust, and Python in supporting tau. Wow!

Learn Enough Python to Be Dangerous

À propos of the final language example in the previous item—namely, Python—I made extensive use of the tau constant from Python’s standard math library in my recently published tutorial Learn Enough Python to Be Dangerous (book, videos, and online course, including the book’s print edition). In my previous tutorials on JavaScript and Ruby, I had to define tau by hand, so it was deeply satisfying this time to have the support of the language itself. As noted in the book’s free first chapter, Python was the first language I really loved, and it’s great to get a little love back in return!

SLMath visit, Tau Day puzzle, and matching donations

On a recent trip to the San Francisco Bay Area, it was my great pleasure to visit the Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) on the campus of the University of California, Berkeley. I was there at the invitation of Uta Lorenzen, Assistant Director of Development, who greeted me wearing her own Official Tau Shirt! (As an extra bonus, and as Uta herself pointed out, her first name is an anagram for “tau”.)

Michael Hartl with Uta Lorenzen at SLMath

As you can see if you look closely at the image above, the friendly folks at SLMath also gave me my own snazzy Tau Day medal, another of which will be awarded to the winner of the Tau Day Puzzle Contest (one day left to solve it!).

Tau Day medal from SLMath

Thanks to Uta and to SLMath Director of Advancement and External Relations Annie Averitt for being such enthusiastic and gracious hosts during my visit. As noted above, generous SLMath supporters are matching donations made through Tau Day 2023. I hope you’ll join me and donate to SLMath/MSRI if you’re in a position to do so. Twice as many donations, twice as much pie!

Thanks again

Thanks again to everyone who has supported tau over the years. Here’s to many more years to come!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2022

Happy Tau Day, everyone! It’s been a dozen years now since the original publication of The Tau Manifesto, making it a dozen years since the true circle constant finally got a proper name:

\[ \tau = \frac{C}{r} = 6.283185\ldots \]

As usual, I’ve made minor updates to The Tau Manifesto itself, which is available both online and (as of last year) as a print edition. And as always, you can show your support for tau by wearing an Official Tau Shirt.

There have been exciting developments every year since the first Tau Day, and this year is no exception. Here are some of the highlights:

Read on for more details about all these happenings. Enjoy!

Elon Musk, Tauist

In a surprise but most welcome tweet, Elon Musk—entrepreneur extraordinaire and currently the world’s richest person—expressed his support for the true circle constant.

Responding to his own tweet about the (reduced) Planck constant $\hbar$ (which is Planck’s constant $h$ divided by… umm… $2\pi$), Elon tweeted the rallying cry “tau > pi”:

Elon Musk tweets 'tau > pi'

As noted in the State of the Tau 2020, “tau > pi” has the virtue of being both literally and rhetorically true. Furthermore, as noted in the State of the Tau 2019, Tau Day is actually Elon’s birthday as well! If you have a Twitter account, please join me in wishing Elon happy birthday (and happy Tau Day) by retweeting this greeting from @TauDay:

Happy birthday to @elonmusk! 🥳 And happy #TauDay, too! 🤓

By the way, as an additional bit of fun, someone responded to Elon’s tau tweet with a version of the Tuxedo Winnie the Pooh meme:

Winnie the Pooh pi, Tuxedo Winnie the Pooh tau

One might even call the fancy tuxedo version the Tau of Pooh!

Das Tau-Manifest: The Tau Manifesto in German

Tau Day 2022 sees the publication of yet another translation of The Tau Manifesto, this time into German: Das Tau-Manifest by Axel Scheithauer, Jonas Wagner, and Johannes Clemens Huber. Thanks to all three for their great work. Vielen Dank!

Das Tau-Manifest

The German translation joins translations of The Tau Manifesto into Spanish, French, Italian, Portuguese, Russian, and simplified Chinese. Please let me know if you’d like to add another!

MSRI Tau Day puzzles

The Mathematical Sciences Research Institute has been offering up a series of four Tau Day puzzles in honor of the big day. Thanks to MSRI for the support!

Tau (again) in xkcd

Tau has made yet another appearance in the popular webcomic xkcd, this time in a strip called Symbols:

xkcd strip 'Symbols' includes a reference to tau

By the way, here’s an explanation of what the full strip means in case you have any questions (I sure did!).

theoremoftheday unearths a gem

A recent tweet from theoremoftheday linked to the 2011 article Pi is still wrong by mathematician Qiaochu Yuan. Yuan quotes a 2007 (and thus pre–Tau Manifesto) blog comment from Fields Medalist Terry Tao, which acknowledges that $2\pi$ is a fundamental constant while suggesting the possibility that $2\pi i$ may be even more fundamental:

It may be that $2 \pi i$ is an even more fundamental constant than $2 \pi$ or $\pi$. It is, after all, the generator of $\log(1)$. The fact that so many formulae involving $\pi^n$ depend on the parity of $n$ is another clue in this regard.

This is indeed an enticing possibility. But of course in many contexts what is needed is a real number, not an imaginary one, suggesting the importance of the magnitude $| 2\pi i | = 2\pi$—which of course is none other than $\tau$.

As Yuan elaborates:

The $2 \pi$ here is precisely the circumference of a unit circle, which is distinguished among all circles because in $\mathbb{C}$ it is the only circle of positive radius closed under multiplication… and is responsible for all appearances of $2 \pi$ in mathematics that I know of.

It may also be worth noting that Terry Tao himself has both the perfect credentials and the perfect name to promote $\tau$, so I’m hopeful that someday he may join MIT, Google, Python, Bob Palais, Vitalik Buterin, and Elon Musk in supporting tau. (Terry even lives in my own hometown of Los Angeles, so if anyone out there knows him, please let him know I’d be happy to meet up sometime!)

1,000 decimal places from memory

On Tau Day 2021, Jarom Watts performed the remarkable feat of writing down 1,000 decimal places of $\tau$ from memory. Jarom’s time-lapse video is definitely worth checking out:

To memorize the digits, Jarom used a memory palace technique based on locations in the city of Pasadena, which he chose as an homage to the location of Caltech, one of Pasadena’s most famous institutions and my own graduate alma mater.

Jarom’s eventual goal is to get up to 10,000 digits and perhaps set an official Guinness World Record. Good luck, Jarom!

Clever numbering and a new dedication

Scott Steinhauser noticed that, after all the revisions and expansions of The Tau Manifesto over the years, the number of the section that originally announced Tau Day had made it all the way to 6.3—that is, it immediately followed Section 6.2. Scott thought this was too good an opportunity to pass up, and suggested calling it Section 6.28 instead. After thinking about it for a bit, I decided he was right!

Section 6.28: Tau Day

In fact, inspired by this development, I decided to keep going, extending the numbering all the way to Section 6.283185, which is a new dedication to one of my favorite teachers:

The Tau Manifesto is dedicated to Harry “Woody” Woodworth, my eighth-grade science teacher. Although I gratefully received support from many teachers over the years, Woody believed in my potential to an extraordinary, even irrational (dare I say transcendental?) degree—confidently predicting that “someday they’ll be teaching the ‘Hartl theory’ in schools.” Given how many teachers have reached out indicating their support for and teaching of the material in The Tau Manifesto, I suppose in a sense Woody’s prediction has now come true.

Thanks to Scott for the great idea!

Thanks again

Thanks again to everyone who has supported tau these last 12 years. Here’s to many more years to come!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2021

Happy Tau Day 2021, everyone! This June 28, it’s time once again—11 years since the original publication of The Tau Manifesto—to celebrate the true circle constant, tau:

\[ \tau = \frac{C}{r} = 6.28\ldots \]

As usual, this annual State of the Tau newsletter includes an overview of the main tau developments since last year’s Tau Day. Some highlights from the past year include:

Update: “$\pi$ Is Wrong!” author Bob Palais passed along an announcement that Berkeley’s Mathematical Sciences Research Institute (MSRI) is observing Tau Day with a “Double The Pie/Double Your Donation” fundraiser (where a generous MSRI supporter has offered to double up to $500 of your donation). You can support MSRI via this donation link, which features a nice tau graphic in honor of the day.

Read on for more details. Happy Tau Day!

In honor of Tau Day 2021, I’ve prepared a print edition of The Tau Manifesto suitable for display on a desk, coffee table, or other surface of your choice:

The Tau Manifesto Print edition

Check out the pricing on The Tau Manifesto Amazon page for a bit of an inside joke. Also, if you’re a fan of The Tau Manifesto, please leave an Amazon review and let people know it!

Français, Português

Since Tau Day 2020, volunteer translators have produced two new translations of The Tau Manifesto, into French and Portuguese:

The French and Portuguese translations of The Tau Manifesto join versions in Spanish, Italian, Russian, and simplified Chinese. Please let me know if you’d like to add another!

Rust, .NET, and Boost

The last year saw tau adopted by the Rust language, Microsoft’s .NET framework, and the popular Boost C++ libraries:

Tau in Rust

Tau in .NET

Tau in Boost

One of the replies to the Rust tweet shared a comment that has become a bit of a tau theme:

the day i learned about tau is the day trigonometry finally made sense to me. the whole time before i was wondering why you always needed two pis for everything and it bugged me so much.

Trigonometry makes sense

Happy to hear it!

Google holiday

Google has long “known” about Tau Day in the sense that the top search result has reliably been tauday.com, but in the last year I discovered that it also really knows about Tau Day:

Tau Day at Google

Amazing! Search for “tau day” and see for yourself. (Can a Tau Day Google Doodle be far behind? Let’s hope it happens!)

Mathstreet Boys parody

Shortly after Tau Day last year, a music video called “Larger Than Pi” appeared on YouTube. A parody of the song “Larger Than Life” by best-selling “boy band” the Backstreet Boys, “Larger Than Pi” explains why $\tau$ is better (larger) than $\pi$:


I’m amazed at all the creative and talented people who have picked up the tau ball and run with it. Fantastic work!

SMBC, again!

Long-time friend of tau Zach Weinersmith, creator of the popular comic Saturday Morning Breakfast Cereal (SMBC), managed to include tau references in not one but two comics this past year:

SMBC Proposed Number Improvements

(You have to love seeing the symbol $\pi$ applied to a new constant because it’s “no longer in use”—implying that, in the world of the strip, $\tau$ as the circle constant has triumphed completely.)

SMBC Bar

I might even deserve a little credit for the “$\tau$-bar” joke in this one, since Zach and I had the following interaction on Twitter back in February:

SMBC Bar joke via @mhartl

Much thanks to Zach and SMBC for the continued support!

Tau and alien intelligence

An alert Twitter user passed along a link to an astrophysics paper, “Planck Frequencies as Schelling Points in SETI”, that contains a footnote referencing tau:

MIT Admissions tau blog post

I’ve long considered the possibility that our planet’s adherence to pi might be a source of embarrassment if we ever encounter alien intelligence. It’s nice to see the authors of this paper hint at the same possibility!

Update: Bob Palais points out that he voiced this same concern in “$\pi$ Is Wrong!”:

What really worries me is that the first thing we broadcast to the cosmos to demonstrate our ‘intelligence’ is 3.14… I am a bit concerned about what the lifeforms who receive it will do after they stop laughing at creatures who must rarely question orthodoxy. Since it is transmitted in binary, we can hope that they overlook what becomes merely a bit shift!

That must be what originally alerted me to this issue!

MIT Admissions blog post

Continuing a long tradition of support from the Massachusetts Institute of Technology, the MIT Admissions website published a blog post in honor of tau by MIT undergraduate Paolo A.:

MIT Admissions tau blog post

The occasion was blog post number $6283 \approx 1000\tau$, which I think is a great way to mark that impressive milestone. Thanks to Paolo for his lucid exposition and enthusiasm!

Tau guerrilla marketing

Tau supporter Neal Donnelly writes:

I read your Tau Manifesto late last year and was immediately converted. With Tau Day right around the corner, I decided to make some business cards that I could hand out to people in Prospect Park on the Sunday before Tau Day. I tried to fit enough of the case for tau on a business card to pique someone’s interest to go read the rest of the manifesto.

Neal was kind enough to give me permission to share the design for “tau on a business card”:

Tau on a business card

This is great guerrilla marketing for tau. Thanks for the support, Neal!

Update: With Neal’s kind permission, the source files for the cards are now available here. Neal recommends using MOO for printing: “The files are all made with their templates and to their specs, so if people just upload the print PDF to the MOO website it should work seamlessly.” Please feel free to make and distribute your own!

In memoriam: John Conway

Mathematican John Conway Photo credit: Bob Palais, 2016

Finally, I’d like to take a moment to remember the legendary mathematician John Horton Conway. Original “$\pi$ Is Wrong!” author Bob Palais writes:

It just occurred to me for possible updates to include a recognition/tribute to the late John Horton Conway, who died earlier in the year [2020] and who was an early supporter-in-spirit of the right circle constant. I thanked him again the last time I visited in 2016.

A prolific and incredibly creative mathematician, John Conway also had the rare distinction of having his work break through into popular culture, via his iconic Game of Life. For years, the favicon on my personal website has been a Game of Life glider as an homage to Conway’s work (based on a proposal by computer hacker Eric Raymond):

Game of life glider

As part of discussing Conway’s support for the right circle constant, Bob Palais passed along a 2008 Physics World article called “Constant failure” by Robert P Crease. In the article, Crease asks, “Would we lose any beauty and economy by using this new constant [equal to $2\pi$]?” (emphasis added):

I posed this question to the Princeton University mathematician John Conway, one of the most creative mathematicians working today. Conway, it turned out, had strong feelings on the subject. “$\mathbf{2\pi}$ is obviously the correct constant!” he told me immediately — although he also told me of arguments, which he did not find persuasive, for a third option, $\pi/2$.

I don’t know if Conway ever heard about tau or if he approved of my choice of notation, but it’s gratifying to know he supported The Tau Manifesto’s core thesis that the right circle constant is $C/r$. And now we’ve got a quote to prove it:

“$\mathbf{2\pi}$ is obviously the correct constant!” —John Conway

Requiēscās in pāce, professor. You will be greatly missed.

Thanks!

Thanks again to everyone who has supported tau these last eleven (!) years. Here’s to many more years to come!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2020

Happy Tau Day 2020, everyone! If you’re celebrating Tau Day on social media, don’t forget to use the hashtag #TauDay. :-)

On June 28, 2010 (6/28/10 in the American calendar system), I published the first edition of The Tau Manifesto, thereby giving the circle constant $C/r$ a name and inaugurating the very first Tau Day. On this 10th anniversary of that fateful day, I’d like to thank the thousands of math fans, science nerds, computer geeks, and fellow tau travelers who have joined me in this quirky, quixotic quest to recognize, honor, and celebrate the true circle constant, $\tau = C/r = 6.283185\ldots$

Amazingly, even after ten years, tau isn’t remotely out of steam—if anything, it continues to gain strength. Indeed, this past year saw the biggest media coverage of tau yet, a new round of Tau Manifesto translations, and endorsements from some of the biggest institutions in science and mathematics.

N.B. You can still get the latest version of the Official Tau Shirt for a limited time. You can also sign up for the Tau Manifesto email list here.

Tau in The Wall Street Journal

On the occasion of Half Tau Day (a.k.a. Pi Day) this year, tau reached a new milestone: full-length coverage in one of the best-known mainstream news sources. In honor of that day, The Wall Street Journal published “For Math Fans, Nothing Can Spoil Pi Day—Except Maybe Tau Day” by Robert McMillan, which prominently featured both me and original “Pi Is Wrong!” author Bob Palais. (In case you don’t subscribe to The Wall Street Journal, you can find an archived copy of the article here.)

Tau in the Wall Street Journal" target="_blank

Participating in the story was terrific fun, and I’d like to thank Robert McMillan for his great work. Although in many ways we’re still in the beginning of this little movement, tau has already exceeded my wildest expectations—when I first published The Tau Manifesto in 2010, I never would have guessed that someday I’d get excited messages from far-flung family and friends saying, “Hey, I just saw you in The Wall Street Journal!”

Italiano, на русском языке, 简体中文

Although recognition by a major media outlet like The Wall Street Journal is a welcome confirmation of our efforts, tau has always been a true grassroots movement. One sure indication of such grassroots support emerged in the past year: full (and 100% volunteer) translations of The Tau Manifesto into not one, not two, but three additional languages!

Adding to the excellent Spanish translation by Juan Guijarro Ferreiro, the Tau Day website now features translations of The Tau Manifesto into Italian, Russian, and simplified Chinese:

I’m deeply grateful for these wonderful efforts, which underscore how mathematics—and hence tau—really is a global community. Thanks for all the great work! (By the way, if you’re interested in translating The Tau Manifesto into another language, please let me know!)

Site Redesign

With links to all the new translations, the menus on the Tau Day website were getting awfully cluttered, and the site was long overdue for a redesign. In particular, while the original Tau Manifesto launched in a world where the iPhone was only three years old, in today’s world pretty much every website has to look good on mobile devices to remain relevant.

Accordingly, I and my Learn Enough cofounder Lee Donahoe (but mostly Lee) redesigned the site to work better on smaller devices by increasing the font size, breaking up longer equations, and switching to a menu system that works well whether you’re browsing on a small smartphone or on a giant desktop. There are a lot of different devices and design constraints, so we’ll no doubt continue tweaking things for a long time to come, but it’s already a major improvement over the previous design. Thanks to Lee for the help!

New Computer Language and Other Public Support

The last year saw the addition of tau to many computer languages and frameworks (adding to a list that includes Python, Modula-2, and many others):

Other support came both from an unexpected direction and from an old friend. Vitalik Buterin, cofounder of the Ethereum smart-contract platform, unexpectedly boycotted Pi Day because “tau day is better”. Thanks for the support, Vitalik! Fellow tauists everywhere appreciate it.

Vitalik Buterin supports tau" target="_blank

Meanwhile, known Friend of the Tau Saturday Morning Breakfast Cereal (SMBC), a popular webcomic that has featured tau before, included a sly tau reference in the May 20, 2020 comic “Social”. In the final panel, a smart and savvy computer user sports a T-shirt bearing the statement $\text{“}\tau > \pi\text{”}$—which is both metaphorically and mathematically true.

SMBC Tau Shirt" target="_blank

Incidentally, that shirt is real! Indeed, as yet more evidence of tau’s grassroots nature, there are many different variations, and I had absolutely nothing directly to do with any of them.

Tau Day 2019 Roundup

Finally, I’d like to review some of the highlights from Tau Day 2019.

Found on Instagram: a version of the popular Drake meme template, in this case featuring Drake looking on with disdain at a bunch of pi formulas and then with approval at the same formulas featuring tau.

Drake Meme Pi Tau" target="_blank

The Massachusetts Institute of Technology (MIT) continued its long-running tau support with “Three cheers for double Pi!”

MIT Tau Day 2020" target="_blank

Meanwhile, the Wolfram|Alpha Twitter account offered a tau-tology in honor of the day. As an enthusiastic user of Wolfram Mathematica back in my graduate-student days, this one meant a lot to me!

Wolfram Alpha Tau Day 2020" target="_blank

Thanks!

Thanks again to everyone who has supported tau these last ten years. Here’s to many more years to come!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2019

Happy Tau Day 2019, everyone!

On this June 28 (6/28 in the American calendar system), thanks for joining me in the annual celebration of the true circle constant, $\tau = C/r = 6.28\ldots$

A special thank-you goes out to anyone wearing an Official Tau Shirt today. You can post pics or any other tau-related material on Instagram #TauDay or Twitter #TauDay.

Spanish Version

The tau news I’m most excited about this year is a full translation of The Tau Manifesto into Spanish by tau supporter Juan Guijarro Ferreiro. You can find the result, El Manifiesto Tau, on the Tau Day website. ¡Muchísimas gracias, Juan!

Tau Birthdays

Some pi partisans occasionally brag about how “Pi Day” (3/14) is the birthday of Albert Einstein, so it’s perhaps worth noting that Tau Day is the birthday of another great 20th-century physicist: Maria Goeppert Mayer, who won a Nobel Prize in Physics for her groundbreaking work on the nuclear shell model.

Long-time tau supporter Joseph Lindenberg has pointed out that Tau Day is also the birthday of famed entrepreneur and literal rocket scientist Elon Musk.

On this 9th annual Tau Day, please join me in wishing happy birthday to Professor Goeppert Mayer and Mr. Musk!

A Tau Conversion

Tau Manifesto reader Jason Brown passed along a delightful tau essay that I’d somehow missed all these years: “My Conversion to Tauism” by Stephen Abbott, which appeared in the magazine Math Horizons in 2012. Professor Abbott is a mathematician at Middlebury College and author of the outstanding textbook Understanding Analysis, making his endorsement especially gratifying. I particularly appreciated this line from the essay:

“The Tau Manifesto” is an entertaining read, so entertaining in fact that you don’t immediately notice how utterly compelling it is.

Thanks, Professor Abbott! I’m glad you liked it. :-)

Internet Trivia Famous

My friend Alex Wood reports on an exchange involving an Internet trivia game:

My girlfriend, reading me trivia questions: “According to a manifesto written by Michael Hartl—”

Me: “Tau”

You’re internet trivia famous, man 😂

A Comics Theme

Continuing a theme set by xkcd & SMBC, on October 13, 2018, the comic strip Sally Forth prominently featured tau:

Sally Forth Pi vs. Tau" target="_blank

Thanks to alert reader and long-time tauist Skona Brittain for the heads-up!

Speaking of SMBC, tau also makes a cameo appearance in the strip “Mega-Pi” about a proposed mathematical constant equal to two million pi (i.e., one million tau).

Another Computer Language

The popular Unity video game engine now includes tau as a pre-defined constant, thereby joining languages such as Python, Processing, and Modula-2. (Still waiting for Ruby to join the party, though!)

Tau Day 2018 Celebrations

Finally, here’s a short summary of some of the high-profile celebrations of Tau Day from last year.

Museum of Science

Joseph Lindenberg passed along this report of the Museum of Science in Boston holding a Tau Day fundraiser, with a benefactor offering to match donations. (The campaign is from last year, but appears to be active, so I think you can still donate if you like.)

The Museum of Science also sponsored tau-themed yoga classes at 6:28, both a.m. and p.m.!

Massachusetts Institute of Technology

Speaking of the Boston area, the official MIT Twitter account sent out a tweet in honor of Tau Day:

MIT Tau Day 2019" target="_blank

Thanks, MIT! Now if only either of my own almae mātrēs would show tau such love…

SciShow

The hugely popular science-themed YouTube channel SciShow (5.7 million subscribers as of this writing) featured an outstanding “Happy Tau Day!” video. Thanks to SciShow for the support!

SciShow Tau Day 2018" target="_blank

SciPress

Swiss open-access academic publisher SciPress ran a Twitter poll on Pi vs. Tau in which, appropriately enough, tau was around twice as popular as pi!

SciPress poll Tau Day 2018" target="_blank

(I neither retweeted nor voted in the poll, so that’s about as unbiased as a Twitter poll can get!)

Onward & Upward

That’s it for this year! Thanks again for all the enthusiasm and support for this quirky little project.

Happy Tau Day, everyone!

State of the Tau 2018

Happy Tau Day 2018, everyone! Thanks for joining me in this annual celebration of the true circle constant, $\tau = C/r$.

I hope you’re all prepared with twice as much pie. 😋🥧🥧

As is my usual custom, I’ve prepared a State of the Tau update summarizing the various tau happenings over the past year.

Hypersphere Update

I’ve substantially revised and updated “Getting to the bottom of pi and tau”, especially the section on hyperspheres, including a brand-new section on recurrences. It’s more mathematically challenging than the rest of The Tau Manifesto, but of course this can be a feature. Go ahead and take a look if you’re in the mood for a challenge!

Tau Day 2017 Celebrations

June 28, 2017 proved to be the most eventful Tau Day since the original Tau Talk in 2011. First of all, I was hosted by Googler Kevin Oberlies and the other gracious folks at Google’s Los Angeles office as part of their “Talks at Google” series. The result is a beautiful HD update to the 2011 version of the talk:

After finishing the presentation, I and some fellow tauists adjourned for lunch, where the Google dining staff had prepared a special surprise for us—tau-themed cupcakes!

Tau cupcakes" target="_blank

Perhaps the greatest highlight of the day was finally meeting Bob Palais, author of the original “π Is Wrong!” article that planted the seed for The Tau Manifesto back in 2001. Bob attended the talk at Google and then came to a Tau Day party I hosted that evening. Here we are in our matching Tau Shirts:

Michael Hartl and Bob Palais in Tau Shirts" target="_blank

We celebrated late into the night with twice as much pie. Thanks to everyone who made Tau Day 2017 so memorable!

The Chad Hartl–Palais Constant

In March 2018, just before Half Tau Day, I was pleased to learn (via Joseph Thiebes) about a fun new tau meme making the rounds online. Created by mathematician Diego Vera, it’s titled “The Virgin Archimedes’ Constant vs. The Chad Hartl–Palais Constant”, and is based on the famous Virgin vs. Chad meme template. Here it is, lightly edited to keep in line with Tau Day’s family-friendly G rating:

Virgin Pi vs. Chad Tau" target="_blank

You can find Diego’s original version (rated PG for language) here. Thanks to Diego for the great meme work, and to Joseph for giving me the heads-up about it!

Euler’s Near Miss

Did you know that the great Leonhard Euler almost settled on using $\pi$ to mean $C/r$ instead of $C/D$? Oh, how much confusion that would have spared us! Check out this fascinating video from wildly popular math YouTuber 3Blue1Brown on the subject:

Breaking Mainstream

Recognition of tau as the true circle constant continues to grow. OG tauist Wyatt Green sent this encouraging field report:

I just wanted to report to you that my dad emailed me this link: “Forget Pi Day. We should be celebrating Tau Day.”

Tau Day has crossed the barrier from esoteric geek conversation to links that family members forward to each other. I feel this is a special accomplishment—a breakthrough into the mainstream.

I also learned via a tweet from Sarah Jeong about an article at The Verge called “Stop celebrating Pi Day, and embrace Tau as the true circle constant”. It’s exciting to see this idea taking root!

Here are the full attributions for reference:

Tau Shirt Sighting

Finally, as usual I’ve relaunched sales of the Official Tau Shirt for a limited time (through Monday, July 2 at 8 p.m. Pacific). It’s an international phenomenon! For example, Johann Swanepoel from South Africa writes:

See attached, me proudly wearing my Tau shirt at the weekly parkrun in George, Western Cape, RSA.

Johann Swanepoel wearing a Tau Shirt on a parkrun" target="_blank

Thanks to Johann and all the other tauists around the globe for making Tau Day and The Tau Manifesto a continuing source of amusement and joy!

Happy Tau Day!

Till next year,

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2017

Happy Tau Day, everyone!

We’ve come a long way since the launch of The Tau Manifesto in 2010, and this year saw continued progress and interest in τ, the true circle constant.

In case you’re short on time, here are three quick action items:

  1. Join me and fellow tau enthusiasts at the official Tau Day 2017 party at Urth Caffé in Santa Monica, California.
  2. Support Ryan Brancheau’s Tau Euro Magnet Kickstarter. (I’m a backer, but I don’t have any financial interest in the project.)
  3. Get your Official Tau Shirt now for a limited time.

There are many ways to celebrate Tau Day, of course, and I hope you’re having fun.

I’m celebrating this year by giving an updated version of the original Tau Talk at Google’s Los Angeles office in beautiful Venice, California. Joining me there will be the original “π Is Wrong!” author Bob Palais as a special guest!

The Google event is closed to the public, but (as noted in the action items above) anyone in the Los Angeles area is welcome to join me and fellow tau enthusiasts for the official Tau Day 2017 party.

The plan, as usual, is to eat twice as much pie!

Tau in Scientific American

Just in time for Tau Day 2017, Scientific American has published “The Tao of Tau”, an exploration of the use of the letter tau in science, engineering, and mathematics. The article opens with an acknowledgment of the true circle constant:

“It is lamentable that there’s no famous dessert named ‘tau,’” Michael Hartl told me recently at a sunny, stylish café in Venice, California. He reluctantly admitted that pi, the constant approximately equal to 3.14, has this one advantage over tau, a number he introduced to replace it.

Read the whole thing there. Congratulations to author Elizabeth Landau on a job well done!

Tau in Python

One of the most exciting tau events this year involves the Python programming language, one of the most popular and powerful languages in use today.

Although nowadays I’m better known for my contributions to the Ruby community, Python was actually the first programming language I really loved.

It is therefore with great pleasure and pride that I announce the inclusion of tau in the latest version of Python. That’s right—after some lively debate, the BDFL of Python, Guido van Rossum, decided to include tau as part of the official math library in Python 3.6:

>>> from math import tau >>> tau 6.283185307179586

Go forth and wield tau, O brave Pythonistas!

Tau N Pi

Another welcome tau contribution came via the son of reader Bobby Cieszki, who created a haunting parody of Kid Cudi’s song “Day ‘N’ Nite” called “Tau N Pi”. Give it a listen—it’s really quite extraordinary.

Key Lime Tau

Last year I mentioned that two breweries (Hawkshead Brewery in the UK and Crooked Stave here in the US) had collaborated to bring the world Key Lime Tau beer. Sounds great, right?

Alas, I soon discovered that it is rather hard to come by.

Well, tauist Richard Soderberg took this as a challenge. He diligently tracked down a vendor, and procured for me a generous supply.

Michael Hartl with Key Lime Tau beer" target="_blank

Verdict: Deliciously sour, and worthy of its name!

Thanks, Richard!

Tau art

Tom Magliery reports on an art project he created involving a collage of numbers—found in the wild, so to speak—assembled to form the digits of tau:

Tau digits collage" target="_blank

Cool!

Los Alamos National Labs

On Pi Day (or, as I prefer to call it, Half Tau Day), Los Alamos National Labs acknowledged tau in its Bradbury Science Museum newsletter article called “Celebrate Pi Day on March 14 (3.14)”:

Pi and controversy (Didn’t see that coming, did you?)

Back in 2001, Bob Palais, a math professor at the University of Utah, wrote an opinion piece for The Mathematic[al] Intelligencer called “π is Wrong!” Apparently, the counterargument against pi is that it is often used as 2π for equations, so why not just use 6.28 instead of 3.14?

That call reemerged again in 2010, when Michael Hartl wrote a book [sic] called The Tau Manifesto making a similar argument and offering up the name of “tau” as the shorthand of 2π or just τ as its symbol.

He’s called for an annual Tau Day on June 28 (6/28 on the American calendar) to raise awareness of the tau concept.

In case you don’t have enough interest to absorb the contents of his book [sic], Michael’s website includes two videos explaining the concept of tau in both short (14 minutes) and long (51 minutes) versions to bring you up to speed.

Dutch newspaper article

Alert reader Wouter Vink passed along this remarkable sighting of tau in an article from a Dutch newspaper:

Tau in a Dutch newspaper" target="_blank

I can’t read Dutch, but this has to count as a good sign. Tau continues to be an international phenomenon!

Tau Euro Magnets

Tauist Ryan Brancheau has launched a tau Kickstarter to make European-style oval magnets with 6.28 in the middle and further digits around the side. Let’s see if we can get Ryan’s project to tip!

Tau Euro Magnet" target="_blank

Tau Shirts

Finally, as usual I’ve relaunched Tau Shirt sales as part of the Tau Day celebrations.

To paraphrase Yogurt from the movie Spaceballs:

Merchandising! Merchandising! Where the real money from the Manifesto is made!

Supporting tau is a labor of love, of course, and it isn’t exactly a major profit center. But you keep asking for tau shirts, so I keep selling them!

Tau Shirt" target="_blank

Tau Day 2017

Thanks to all the tauists out there who continue to make this quirky project so much fun. Hope to see you at the party.

Happy Tau Day!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2016

Happy Tau Day, everyone! It’s hard to believe it’s already been six years since The Tau Manifesto launched and the real battle against pi’s supremacy began.

I don’t keep careful statistics, but I can confidently state that awareness of tau is enormously widespread. As an active member of the Caltech alumni community, for example, I frequently meet Caltech undergraduates, and they’ve virtually always heard of Tau Day.

Similarly, I’ve found in the programmer community that a fair fraction have heard of tau. In my own little corner of tech, every so often someone will freak out upon realizing that the authors of the Ruby on Rails Tutorial and The Tau Manifesto are the same person. Indeed, today I hope to blow more than a few such minds, because I’ve just launched the new edition of the Ruby on Rails Tutorial book—on Tau Day!

One cool thing is seeing people wearing the Official Tau Shirt, which as usual is available for a limited time (sales expire tomorrow). For example, my mother reported seeing one on an elementary school student in Orange County, California, last year. And just a couple of weeks ago I was driving through downtown Los Angeles when I saw a woman wearing a Tau Shirt. I recognized her as my friend Carol Hoffstedt, so I rolled down the window and said, “Hey, Carol! You win!” I mean, what are the odds!?

As in previous years, people continue to amaze me with the incredible variety of creative projects inspired by tau. For example, a tauis at MIT, told me about a “Tau Day Hack” involving “Tau on the Cow” (don’t ask me exactly what it means!):

MIT Tau on the Cow" target="_blank

I’m glad to see MIT picking up the tau ball and running with it—and challenge my fellow Techers at Caltech to do the same. (Hint, hint!)

Finally, the ever-enthusiastic Joseph Lindenberg passed along this fantastic bit of tau culture found in a most unexpected place: a specialty beer from Hawkshead Brewery called Key Lime Tau!

Key Lime Tau beer" target="_blank

As described on its website:

The [Key Lime Tau] beer, originally a collaboration brew with Crooked Stave (USA), is our take on a key lime pie. It was brewed on both sides of the Atlantic, hence two ‘pies’ and is 6.28% in strength.

6.28% in strength! How can you not love that?!

Alas, it looks like Key Lime Tau beer is pretty hard to come by, and I haven’t yet procured any for myself, but for next year I’ll do my best to fulfill the promise implicit in this lovely poster, and drink Hawkshead Key Lime Tau on International Tau Day!

Hawkshead Key Lime Tau poster" target="_blank

Until next year—Happy Tau Day!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2015

Happy Tau Day 2015! Interest in the true circle constant (τ = C/r = 6.283185…) and The Tau Manifesto continued unabated this year, highlighted by a surge of attention on the “Pi [Half Tau] Day of the Century” (3/14/15). (Tau will have its revenge on 6/28/31—party at my place!) As one of the leaders of the “opposition”, I was invited to the Pi Day festivities at the Exploratorium in San Francisco—the organization that originally created Pi Day—but I was on vacation in Barcelona at the time and was unable to attend. (I know, rough life!) That the invitation was proffered in the first place is an excellent sign, though, as it serves as proof that even the Paladins of Pi recognize tau as a legitimate rival.

Here are some of the highlights since last year’s Tau Day:

Using tau instead of pi makes math clearer, and thus easier to understand.

Using pi is like having a weird car whose odometer and speedometer display half-miles and half-miles-per-hour, while all the road signs show miles and miles-per-hour.

(The road signs of math are naturally in units of tau.)

So you constantly have to convert between what your car says and what the road signs say. 55 mile-per-hour speed limit? Make sure your speedometer needle doesn’t go over 110. But instead of nice round numbers like 55, imagine the sign says 68.7 miles-per-hour. So your speedometer needle shouldn’t go above… how much? Your trip odometer reads 35.7. So you’ve traveled… how many miles?

Sometimes you must multiply by 2. Sometimes you must divide by 2. And before doing either, you must always stop and decide which to do in this particular case. If you’re driving in heavy traffic, or bad weather, or you’re lost, you don’t want that distraction. The same is true if you’re lost while trying to learn trigonometry.

Thanks for all the support! For me, that makes for a very happy Tau Day.

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

State of the Tau 2014

Happy Tau Day, everyone! This was a huge year for $\tau$, with continued adoption in programming languages and classrooms, appearances in a couple of prominent webcomics (xkcd & SMBC), and a big endorsement from Google. I also received an amazing parable about pi and tau from a precocious high-school student—seriously, give it a read.

Here’s a list of some of the highlights since Tau Day 2013:

I’ve been gratified by the continued enthusiasm for $\tau$ since the launch of The Tau Manifesto in 2010. I especially appreciate the support of Robert Palais, Joseph Lindenberg, Peter Harremoës, Robin Whitty, Vi Hart, and all the tauists who’ve reached out about $\tau$ in the past four years. Here’s to another great year ahead for $\tau$!

—Michael Hartl, Tau Day 2014

State of the Tau 2013

It’s been a big year for $\tau$. When I launched The Tau Manifesto back on Tau Day 2010, I hoped that $\tau$ might strike a chord, but its popularity has exceeded my wildest expectations—due in large part to the efforts of the many ardent tauists who picked up $\tau$ and ran with it. Now three years on, activity surrounding both the constant and the notation continues apace. In honor of Tau Day 2013, I’ve listed below some of the highlights from the last year. Enjoy, and Happy Tau Day!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

Note: I’d like to thank Joseph Lindenberg, Robert Palais, Robin Whitty, and Peter Harremoës for their help in compiling this list.

Radians with tau

State of the Tau 2012

Happy Tau Day, everyone! As a special bonus for Tau Day 2012, I’ve written an exciting new section of The Tau Manifesto called “Getting to the bottom of pi and tau”, which builds an irrefutable case against pi. I also wrote a short feature for CNN.com, published today as “Tau Day: Why you should eat twice the pie”. Finally, although I didn’t have time to host a Tau Day party this year, you can find the video from last year at tauday.com.

What phi sounds like

Michael Blake, creator of the incredible music video What Tau Sounds Like, has honored tau’s fellow fundamental constant phi with What Phi Sounds Like. Known as the “golden ratio”, phi (written as $\phi$ or $\varphi$) is irrational but (unlike tau) is not transcendental, and in fact can be written in terms of the square root of $5$ as follows:

\[ \varphi = \frac{1+\sqrt{5}}{2} = 1.618\ldots \]

(This is just the positive root of the quadratic equation $x^2 - x - 1 = 0$.)

Incidentally, I’ve been told that some mathematicians (especially in Europe) use $\tau$ instead of $\varphi$ for the golden ratio. This introduces a minor notational conflict (easily resolved by using $\varphi$ instead), but it also shows that there is precedent for using $\tau$ to represent a fundamental mathematical constant!

Tau recitation world record

I’m pleased to announce that seventh-grader Ethan Brown recently set a world record by correctly reciting 2012 digits of tau, raising over $3000 for his local library in the process. You can read more about it here. Congratulations, Ethan!

Happy Tau Day,

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto