When I launched the first edition of The Tau Manifesto back on June 28, 2010, I hoped that Tau Day might become a “thing”, but its success so far has exceeded my wildest expectations. With tau featured in places like Apple’s iOS, Google’s official calculator, and the Python programming language, and with Tau Day featured in outlets like Science News and The Wall Street Journal, at this point there seems to be no stopping tau. And it’s all due to the enthusiastic support of tauists like you—those persons of rare discernment who recognize that the true circle constant is C/r:

τ = C/r = 6.283185…

As always, I’ve prepared a State of the Tau update with some of the tau happenings since Tau Day last year. Here’s a brief summary:

• The fourth annual Tau Day celebration from the Simons Laufer Mathematical Sciences Institute (SLMath)

• Some cool tau GPS art

• Twitter/𝕏 roundup

• More tau memes (and a haiku)

See the full State of the Tau 2025 for all the details.

Happy Tau Day!

Michael

Subscribe now

• The Art of Problem Solving

In other news, Tau Day is coming up fast! As in previous years, SLMath, one of the world’s top mathematical research institutions, is planning to run special events for the day, including a puzzle contest and a funding drive. I’ll be proud to contribute again this year.

In past years, we’ve had matching donations from a generous benefactor, but unfortunately the donor is unable to provide matching donations again this year. As a result, we’re looking for someone special to step up with a $6,280 matching gift to inspire even more support for SLMath’s exceptional programs. Interested in being our match donor? Reach out to uta@slmath.org or visit https://www.slmath.org/support to help make this Tau Day 2025 count—twice!

Cheers,

Michael

Subscribe now

Tau, as you’ll likely recall, is the circle constant defined by the equation τ = C/r, a notation first publicly proposed by yours truly in 2010 via the now-infamous math essay The Tau Manifesto. Since radian angle measure is defined by θ = s/r, setting the arc length s equal to the full circumference C shows that θ = C/r = τ is the angle of a full turn of a circle. Setting r = 1, we see that, equivalently, we can think of τ as the circumference of a unit circle. It’s all so easy and natural with τ!

In honor of this semi-auspicious day, I thought I’d share with you an exercise (and a preliminary example) from a two-volume set of books I recently finished studying: The Art of Problem Solving, Volumes 1 & 2. Though nominally aimed at high-school students, AoPS (as it’s abbreviatedly known) is full of material sufficient to challenge even quite experienced students of mathematics.

The full post is fairly involved and involves a lot of mathematical typesetting not well-supported by email clients, so as usual I’ve published the full version on my website at michaelhartl.com:

• An AoPS Problem for Half Tau Day 2025

The short of it is that we can use τ and a little elementary number theory to find a compact and elegant formula for the period of the sum of a sine and a cosine. It is exactly the kind of problem I wanted to know how to do when I started studying The Art of Problem Solving, and which (despite having a Ph.D. in physics) I couldn’t do even a few months before encountering the problem in 2024. This was due not to any deficiency in my understanding of periods of sinusoids, but rather to a weakness in my understanding of elementary number theory.

I hope you enjoy it!

Cheers,

Michael

• How to Prove It by Daniel Velleman

Enjoy!

Michael

Subscribe now

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:

𝜏 = 𝐶/𝑟 = 6.283185…

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:

• The Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) is running their third annual Tau Day fundraiser, with generous matching gifts to double the impact of donations. (details)

• SLMath is also sponsoring not one but two puzzle contests (one featuring an Official Tau Shirt as a top prize), both available on the SLMath Tau Day page. (details)

• I have received reports of continued adoption of tau in various corners of computing, including the Nim systems programming language and an amazing appearance in iOS, the operating system powering iPhone and iPad. (details)

• There were lots of great tau happenings on Twitter (sometimes, though rarely, called 𝕏), including supportive tweets from MIT, Vitalik Buterin, and Elon Musk! (details)

• An alert tauist passed along a vintage Vi Hart video I somehow missed all these years, featuring a wonderful song about tau. (details)

You can find the full State of the Tau 2024 on the Tau Day website. Happy Tau Day!

Michael Hartl
Founder, Tau Day
Author, The Tau Manifesto

• Another Contest Math Problem

The subject is a delightful geometry problem from The Art of Problem Solving, Volume 1.

Enjoy!

Michael

Subscribe now

I’ve got some more updates planned for my math learning project, including a post on a challenging “high school” geometry problem and a review of The Art of Problem Solving, Volume 1. Watch this space for notifications.

In the meantime, now’s a good chance to mention the Official Tau Tee Shirt and the print edition of The Tau Manifesto. Get them now in advance of Tau Day 2024! (How cool is it that Google knows when that is?)

Happy Half Tau Day, everyone!

Michael

Subscribe now

• Time Dilation and the Star Trek Dream

Enjoy!

Michael

Subscribe now

• Solution to a Contest Math Problem

Enjoy!

Michael

Subscribe now

• Math Learning Project Status Update (Intro to Math)

Enjoy!

Michael

Subscribe now

• Pure Mathematics for Beginners

Enjoy!

Michael

Subscribe now

• Resources for Math Learning (Intro to Math)

Enjoy!

Michael

Subscribe now

• Library Genesis

Enjoy!

Michael

Subscribe now

• Personal Strategies for Math Learning

Enjoy!

Michael

Subscribe now

• Personal Goals for Math Learning

Enjoy!

Michael

Subscribe now

In particular, I’m embarking on a major math learning project that I think will be of interest to fans and followers of Tau Day and The Tau Manifesto.1 I’ve recently published the first in a series of posts on the subject, which you can find here:

• Math Learning Project

Enjoy!

Michael

Subscribe now

As noted in the recent 2023 State of the Tau newsletter, I started this Substack both to make tau-related announcements and to discuss math and math learning. Substack has some of the same issues as the defunct platform mentioned in the previous paragraph, though. Moreover, even if (as seems likely) Substack continues to thrive as a business, the thought of having my posts trapped in its proprietary editor makes me deeply uncomfortable.

As a result, my current plan is to publish most posts on my website, michaelhartl.com, which uses the Jekyll static site generator with plain-text posts stored in a Git repository. In order to minimize friction, I expect to use Substack for short summaries and email notifications for the posts but not for the full posts themselves; rather than trying to keep full copies in both places, the canonical version of the full post will be at michaelhartl.com.

This issue didn’t come up with the State of the Tau newsletter since historically I’ve published that both as an email and at tauday.com, but constantly having to keep two posts in sync is simply more trouble than it’s worth. Moreover, publishing the main posts exclusively at michaelhartl.com has the additional advantage of allowing me to use full-strength mathematical typesetting with LaTeX, using both MathJax and my own jekyll-latex plugin.

For example, the online version of this post has a slick inline copy of the time-independent Schrödinger equation here: 😔. Unfortunately, Substack simply isn’t cool enough to manage it, thus the 😔 emoji. (It’s not really Substack’s fault: by design, Substack posts have to render properly inside email clients, so the only LaTeX support they currently offer is centered math, which is rendered with MathJax in browsers and with embedded images in emails.)

One result of this is that, barring a change in policy, posts will generally be available for free at michaelhartl.com.1 Paid subscribers to my Substack will still get concrete benefits, though, including:

• Email notifications for any subscriber-only posts

• The satisfaction of supporting my work financially

• The ability to comment on select posts

• The ability to send me messages by replying to any Substack email

That last bullet point deserves a brief comment. My email address isn’t that hard to track down (or guess), but there’s always a question about whether an unsolicited email would be welcome. In contrast, paid subscribers can reach me through Substack by responding via email to any of these announcements. Perhaps more importantly, paid subscribers are invited to do so, which means you know you won’t be bothering me if you do (at least, not unless you really try—please don’t take this as a challenge!).

So, if you’d like to get the above benefits, please consider upgrading to a paid subscription if you haven’t already.

Subscribe now

In any case, stay tuned for lots of upcoming posts on math and math learning!

Hey Google, when is Tau Day this year?

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:

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!)

Subscribe now

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

• As the result of a collaboration with math YouTuber sudgylacmoe, there is now an amazing animated version of The Tau Manifesto.

• Tau has been added to Liberty Eiffel, a free compiler for the influential Eiffel programming language, and (amazingly) has also been added to that 800-lb. gorilla of modern computing, the Java programming language.

• I published Learn Enough Python to Be Dangerous, which makes extensive use of math.tau from the Python standard library.

• JSCAD, an open-source set of libraries to create 3D and 2D designs using JavaScript, comes equipped with a predefined constant TAU.

• Aleksandr Alekseevich Adamov (who made the Russian translation of The Tau Manifesto) passed along a link to a formalized proof that τ = 2π.

• For the second year in a row, SLMath (formerly MSRI) is running a Tau Day puzzle contest, with an Official Tau Shirt as a prize! In the spirit of “twice as much pie”, generous SLMath supporters are also matching any donations made through Tau Day 2023.

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!

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”.)

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!).

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