Having consumed my share of Costco pies the last few weeks (they’re good, too!), I’m happy to report that it’s Pi Day, celebrated with the following Google Doodle (click on screenshot to go to the Doodle site):

Google itself explains the Doodle here, adding a video and, at the link, a recipe for a scrumptious salted-caramel apple pie. I hope at least one reader makes it:

Happy Pi Day!

Celebrated each year on March 14th (3.14), Pi Day is dedicated to the mathematical constant, Pi. First recognized 30 years ago in 1988 by physicist Larry Shaw, Pi Day observers often celebrate with a slice of their favorite pie in honor of the number’s delicious sounding name.

Notated by the Greek letter “𝛑”, pi represents the ratio between a circle’s circumference (perimeter) to its diameter (distance from side to side passing through the center), and is a fundamental element of many mathematical fields, most significantly Geometry. Though modern mathematicians have calculated more than one TRILLION decimal places beyond the standard “3.14,” pi is an irrational number that continues on to infinity! It’s an important ingredient in the formula for the area of a circle, A=𝛑r².

Today’s delectable Doodle – baked & built by award-winning pastry chef and creator of the Cronut®

Dominique Ansel– pays homage to this well-rounded mathematical constant by representing the pi formula (circumference divided by diameter) using — what else — pie!Go behind-the-scenes of today’s Doodle below!

By the way, has anybody ever proven that pi *must* be an irrational number? Or did it just work out that way?

Note that Pi Day can only apply in parts of the world where they write March 14 as 3/14/20-; most of the world does it wrong, using 14/3/20. Such parts of the world can have NO Pi day, and therefore they don’t deserve pie.

Note, though, that this Doodle’s reach extends much wider than that of a regular Doodle. Only sub-Saharan Africa, South Asia, and, curiously, Norway and Finland lack the Doodle and and, apparently, pies:

Here are the favorite pies of Professor Ceiling Cat (Emeritus); I am leaving out savory pies:

Malgorzata’s fresh cherry pie made with walnut crust

Pear cream-cheese pie

Peanut-butter/chocolate cream pie

Key lime pie, but only when made with real Key Limes rather than bottled juice. The pie is not nearly as good when made with regular (“Persian”) limes. There are only a few places in America where you can get the real thing in a restaurant (Manny and Isa’s in Islamorada Florida, on the Keys, used to be one of them, but I don’t know if it’s still there); but you can make it using the tiny Key limes available in many high-class markets.

Blueberry pie, especially when made at Helen’s Restaurant, in Machias, Maine, where they use lowbush blueberries (the small ones) and heap a mixture of cooked and fresh blueberries into an open-top crust, slathering a thick layer of whipped cream all over the top. Here’s a piece. Hungry?

What’s yours? Anybody eating pie today? I doubt I’ll get the chance.

## 101 Comments

Many proofs of irrationality, with Lambert (1767)usually credited as first.

It’s worse. 𝛑 is transcendantal.

https://en.wikipedia.org/wiki/Transcendental_number

Enjoy the rich sweet pies, those who are indulging. They look far too rich and sweet for me. I’ll take a steak and kidney pie any day.

I had a dentist who used hypnosis along with a mild painkiller in place of novocaine or gas when he worked. He called it “trance & dental medication”.

I’m stealing that. Sorry.

But computable, so representable in a small space.

Our most distinguished Professor Ceiling Cat posted a YouTube video of the proof of pi being irrational right here in WEIT on October 10, 2016

https://whyevolutionistrue.wordpress.com/2016/10/10/why-is-pi-irrational/

I’ve never seen a simple proof of pi’s irrationality (and the video provided in the 2016 PCC(E) blog skips several steps and has a few errors). Proof of its transcendence is much much harder.

e is a much more important constant in many ways, yet gets far less attention.

One of the most beautiful formulas in the universe contains both:

e^{i\pi} = -1

That’s just a special case of the real most beautiful formula in the Universe

e^{iΘ} = cosΘ + isinΘ

relevant cartoon

Inasmuch as π facilitates our understanding and production of pies, it is to be celebrated.

Glen Davidson

I vowed this morning to reduce my calorific intake and lose a few pounds, and then I get a post about Pies, I can’t win.

No you can’t. Not at this site.

I have a favorite pear pie as well. One seasoned with black pepper of all things. It was amazing! Only had it once when a chef friend baked one for sale in another friend’s espresso bar.

Month/Day/Year makes no sense! I gladly forgo pie today for clarity, reason and Common Sense, as one should. The correct way is, of course, Day.Month.Year, small to big. The other way around, big to small, is also acceptable but inferior, because the day date changes faster, and for daily use is more relevant than month or year, and hence should come first. One can also easily either drop the year, or the day, and the sequence still remains intact.

As with miles, yards and inch, Americans are doing it wrong! If the world was just, everyone else but Americans would get pie.

+1000

I remember having to complete two forms to enter the USA: immigration and customs declarations. One was Month/Day/Year and the other was correct.

I have long used Year/Month/Day for repeated filenames, since they then sort in strict time order.

I agree, Y/M/D is very convenient for sorting filenames.

Japan, Korea, and China (and possibly other countries – Taiwan seems likely) typically use Y/M/D in everyday use.

I do that for file names too. The rest of the time I do it the proper way – day month year. The US way makes no sense.

It’s about time the US went metric too.

ISO 8601 is your best friend.

What’s the date on your comment? March 14. That, of course, is why Americans also write 3-14-18, because we say March 14, not 14 March or the 14th of March (the latter is occasionally said, but it’s the exception).

In the UK, at least, you’re supposed to write Wednesday, 14 March 2018, or Wednesday the 14th of March, 2018, so by the numbers it’s 14-3-18.

It’s word order, it can go either way. But if you say March 14 it only makes sense to use the same order when you’re using numbers.

Glen Davidson

I’m in the US, and I always write “14 March”, but I’ve worked in a lot of places where I had to deal with the rest of the world.

Absolutely!

I’ll take y/m/d or d/m/y any day.

The US has this illogical date format. Plus it is a pain sorting/correcting data bases where dates have been entered in the US format either as text or a number format.

Royal pain.

Plus seeing a date like 12/11/18 one never can tell what date is. OK might be obvious in the US, but in Canada it is not.

For many purposes (especially incorporating dates in computer file names), I use the yyyy-mm-dd format, because this doesn’t require elaborate algorithms to sort file names by date.

I spent a number of years working at one of the National Laboratories, and got used to the dd-mm-yyyy format, along with 24-hour time and using SI, especially Celsius. I actually have a stove that is calibrated in Celsius. To bake a pizza, I fire it up eo 220 degrees.

220 degrees Celsius for pizza!? That’s wimpy. Do it like the Italians under the broiler for 2 min.

I get my hand built cob oven up to 550C for Pizza. Take about a minute to cook one to perfection!

For file and folder names, I like year-month-day, as in 2018-03-14. They automatically sort in chronological order.

No big to small is best because it’s easier to sort and it follows the same convention as ordinary numbers (in Western writing systems).

Either way works, whatever is convenient in a context, as there is no way to confuse what the year is, as long it’s written out. You see instantly that year is leading or day is leading, only Americans introduce sheer madness.

No one proved – as far as I know – that pi needs to be irrational. It just is.

But as you surely know, picking a random real number will give you an irrational number with probability of 100%. So, it’s at least far more likely that it would turn out to be irrational.

As you might now as well, pi is not only irrational but also transcendental. (Which very roughly means that you cannot find any polynomial with rational coefficients for which pi would be a root.) I don’t really know right now how the probability of picking a transcendental number out of the real numbers is, but I’m pretty sure it’ll be 100% as well.

“…probability of picking a transcendental number out of the real numbers is, but I’m pretty sure it’ll be 100% as well.”

Yes it’s 100%. The set of non-transcendentals (i.e. algebraics) is a countable infinity, so you just need to accept that the ratio ctble/unctble is somehow the number zero! And that word “pick” maybe means something a bit more technical!

I don’t understand your statement “No one proved – as far as I know – that pi needs to be irrational. It just is.” It’s that word “needs” that you must have a definition of which escapes me.

We just crossed comments …

The word “needs” comes from Jerry’s question which was if there is a proof that the number pi *needs* to be irrational. That’s how I understand his question. Not if it was proven that pi is in fact irrational but if there is a specific reason why pi simply could not be rational.

The “specific reason” is the content of the mathematical proof.

But as a commenter further down said, there indeed appear to be proofs of this – that pi could not possibly have turned out to be rational. And indeed I have found a very nice and simple proof by one Ivan Niven of 1947.

According to Eli Maor in To Infinity and Beyond, it was proved in 1762 by the Swiss mathematician Johan Lambert (pg 50)

You can’t “pick a random real number.” The reals are not compact, so there is no measure for which that statement makes sense. Same for the integers.. you cannot pick a random integer.

“..has anybody ever proven that pi must be an irrational number? ”

Yes, more than 100 years ago.

By the way, the Google bit: “pi is an irrational number that continues on to infinity!” is quite misleading.

In a trivial sense sometimes, every number has decimal representation that “..continues on to infinity!”

Trivially, good old 3 itself is really 3.0000… forever. But hold on, less trivially, every rational number is also, and ‘most’ don’t end in all 0s.

⅓ is 0.33333….

2/7 is 0.28282828….

7002/700 is 10.0028282828 … , etc.

It should instead have said that \pi has decimal which does not eventually repeat periodically. \

‘Periodic if and only if rational’.

Works both ways.

By the way, this proves the impossibility, in the ancient Greek ‘Squaring the circle” problem about geometric constructibility.

More difficult, \pi is transcendental, and any transcendental is irrational. So that would be another, but more difficult, proof of irrationality, but with more info.

I think the question wasn’t if pi is an irrational number. That was indeed proven quite some time ago.

The question (if I understood it correctly) was if it was ever proven that, whatever exact number pi would be, that number could not possibly be rational (note the emphasis on the word “must” in the article).

It’s just that, as I also half-asked just above, I have no idea here what you mean by “needs” and “must”.

My normal usage of those words in this context is that any theorem of mathematics ‘must be true’ or ‘needs to be true’.

You are likely thinking of some other useage??

The ratio of a circle’s circumference to its diameter need not be irrational in non-euclidian geometry, if that is what you mean. But it isn’t a constant either. It varies from circle to circle.

To be a smart-ass, yes, if something is not a number, then it is certainly not an irrational number, no mathematics or even definitions of the technical words needed. Just logic of a pretty basic kind!

And the classical approximation to the (spatial) universe, unless a very crude approximation, in GR, is not going to be Euclidean!

For that matter,

0.99999…”forever”

is exactly equal to 1.

Yes, fortunately I did not claim a rational number is UNIQUELY a periodic decimal!

As I’m sure you agree, 1.000.. is a bit easier to work with, as are both 37/100 and .37 easier than .3699999….. !!

That sort of example is the only instance of non-uniqueness.

My annoying tendency to go on and on is unfortunately showing up here!

The impossibility of “Squaring the circle” comes from pi’s transcendence not it’s irrationality.

The ancient Greeks could construct irrational numbers geometrically easily enough, for example the diagonal of a unit square.

See my reply to 15.

The most intuitive proof that pi must be irrational is to express it as a continued fraction, but several constructive proofs exist.

There’s much to be said for the Taxicab Metric / Geometry. There pi = 4. That’s it. 4. Nobody gets hurt.

As long as the taxi doesn’t crash.

Not in London, it isn’t.

I like my pies to be 50:50 pie:whipped cream.

But that’s a fraction!

A favorite math joke that I tell many of my students is this.

If a pizza has a crust thickness of ‘aa, and a radius of ‘z’, what is its volume?

(pi)zza

Another is to reflect 3.14 in a mirror. It spells PI.E

Darwinwins, that is a very acute and astute, nay,

observation. Incontrovertible! How can someone possibly still doubt the existence of the Great Demiurge after that?stunning‘a’, I guess?

Whoa!!!!!

Wait a second!!!!

If America is the ONLY country that writes dates in MM/DD/YYYY format, doesn’t that make it “American Pi” day?????

Canada writes the dates that way as well. I was taught that way in school. However, you see a mish-mash of both so I never know what’s going on with numerical dates & try to write out the actual day and month instead, as in: March 14, 2018.

Hi Diana,

As a fellow Canadian, the ambiguity & irrationality of mm-dd-yy drives me nuts.

See my comment below:

yyyy-mm-dd is unambiguous and even our American friends know what it signifies.

-evan

And when you express dates that way, numeric and alphabetic order are the same. (As a data person, I appreciate that.)

I remember when I learned how to write the dates the American way in school, my parents laughed & said, “hahahahahahaha she writes the dates like a computer”. It was the 70s.

It still works. Canada is in (North) America.

Oh that was an unfair! NOW I WANT SOME PIE! Fruit pies are the best, and Key lime is the best of the best, but there not a chance in hades I’ll be getting any Key lime pie today, real or otherwise. 😩

Key lime is also my favorite. A great combination of tart and sweet.

I had some this morning and it was delightful.

South Africa has no doodle

at alltoday. I’mdeeplyoffended. As if colonialism wasn’t enough, as if (predominantly) black Africans haven’t suffered enough, they rub it in and deprive us of a Doodle! Those white supremacist ex-Muslim sexist Jewish homophobic racists! Let us startagainst supremacist and racist Google!actionNow I’m wondering: Apart from outright proving the irrationality of pi, when was it first suspected or believed that pi is irrational? Did Archimedes believe in its irrationality?

According to the inerrant Bible 𝛑=3, so we

mightbe wrong, now do we? 🙂Good point! And as we all know, the Bible is completely rational.

And according to the holy trinity 3=1, so the circumference of a circle is equal to its diameter. We can all go home now. Our work here is done.

The ways of the Demiurge are impenetrable, it appears. Pure magic!

Now that the pi is finished, we can set the Biblical sights on Euler’s number. The base of the natural logos! e-ternity!

The ancient Greeks certainly knew about irrationality: Discovering that the diagonal of a unit square had such a length, \sqrt2, was a major human discovery. I don’t think Persian or Indian mathematics knew that.

So I would guess: yes, Archimedes would suspect irrationality of \pi , since he was after the above discovery, and the number was the diameter of a ‘unit’ circle (not a usual term).

Not still an answer to 15, but I noticed in 7 that my last two paragraphs I had mistakenly reversed just before posting, thinking it was better wording. But transcendentalness, or at least something stronger than irrationality, is needed to solve the ‘circle squaring’. Point is that the set of straightedge-and-compass constructible numbers does contain some irrational numbers, e.g. \sqrt2 above, but certainly no transcendentals.

This actually got me thinking (shame on you) and I dug out a book I’ve been meaning to get around to for the last decade or so — Berggren’s “Episodes in the Mathematics of Medieval Islam.” What a surprise. He states that Khayyam (the jug of wine Khayyam himself)thought “the ratio of the diagonal of a square to the side, or the ratio of the circumference of a circle to the diameter should be considered as new kinds of numbers.” That more than just recognizing incommensurability — it’s actually suggesting the expansion of the number system. Getting real, indeed.

Thanks. I had no idea about that. And for the Greeks, they had a new kind of number in the sense of irrationality, but an old kind in being the distance between points in the plane. It would be interesting if somewhere in Islamic parts but before Islam, that wonderful proof of irrationality of \sqrt 2 was discovered independently, maybe even before the Greeks.

The positive reals which are constructible include the rationals and is closed under addition, subtraction, multiplication, division, and square roots. Thus 2nd, 4th, 8th, …. roots of rationals are in there along with sums and products of those. Transcendentals are not constructible, nor are, e.g. cube roots, which shows that duplicating the cube (constructing a cube of twice the volume of given cube)is not cpossible since it would require constructing the cube root of 2.

No Doodle in Portugal and Spain too. Snif, snif.

One of my pet peeves:

Canada is “blessed” with multiple influences so when people here use numeric dating such as 03/04/06, it could mean 3 different possible dates…

The only unambiguous notation should be the ISO standard; yyyy-mm-dd (pick your favorite separator).

Let’s lose the mm-dd-yy convention.

Good news, 2018-03-14 is Pi Day everywhere.

Sadly, in most countries outside the US using our calendar, it is DD-MM-CCYY, hence not everywhere. 14 03 2018 is not really a good approximation, even the Bible does better (if we disregard that 1=3, which -as could be argued- is a ‘special case’).

Exactly; thus the need for the ISO standard. No one country lays claim to it and it is universally understood…

Americans still don’t use the metric system and still have pennies and $1 paper bills, so you aren’t going to get them to change how they write dates! 😉

OK. You’re right.

I’ve changed my mind.

Since Pi is an irrational number, it only makes sense to use an irrational dating system to celebrate its status…

3:14 am on 15th September is 𝜋 minute.

At the federal government level, ISO is required in Canada, but it is sometimes honoured in the breach.

of course the rest of the world has a Pi Day – 22nd July. Which is more accurate. 🙂

I made tart cherry pear pie with almond crust for Pi Day. It turned out quite good. Other colleagues brought apple sreusel pie and chocolate cream pie. Overall a great Pi Day.

I computed pi on my Mac. Now I have an Apple pi.

Now do it using Raspberry Pi.

Great idea. That would be a Raspberry pi^2.

While looking on the internet for the restaurant along the highway between Portland and Astoria that makes excellent berry pies from wild berries, I found this instead:

http://www.onlyinyourstate.com/oregon/best-pie-oregon/

I am a math teacher and we did two classes of pie making yesterday in preparation for today’s lunch. And what happens? A snow day. One more foot. But they’ll be a good treat tomorrow. Don’t even have photos. They all had to be no-bake, cookie crumb crust with pudding and/or cream fillings. Pi exploration/instruction was a cinch compared to recipe reading instruction. That was a nightmare.

You may all go to dd-mm-yyyy, and I will go have some pie.

~ Barn Owl Crockett

“Only sub-Saharan Africa, South Asia, and, curiously, Norway and Finland lack the Doodle…”

The map I see shows South Asia covered, but not central, east, or south-east Asia. Also the Iberian Peninsula, and most of the Caribbean (except for the Dominican Republic and Puerto Rico) are left out.

I just went and stood in line for a $3.14 pizza at Blaze. Unfortunately what seemed to be about half the Northwestern undergrad population seem to have had the same idea, so as my ears started to freeze I gave up and got a pita sandwich from across the street. So I’m piless 😦

I celebrated on 31st of January!

🙂

22/7 is often considered an acceptable approximation for pi (though the not much more complicated fraction 355/113 is far better, matching pi until the sixth decimal place), so those who express the date with the day first (ascending order of unit from day to month to year) could use 22 July as Pi day instead.

A friend was telling me that just yesterday.

1. Cherry pie from Smith’s Farm Orchard in Charlton, NY.

2. Pecan pie (real pecan pie, not just a sugar pie with some nuts on top).

Is Pi a property of our Universe? Can we envision other universes where Pi has a different value?

I don’t think so, because Pi can be derived through pure mathematics without having to actually measure circles, and I don’t believe mathematics is a property of our Universe.

The English were writing the date as dd/mm/yyyy long before America was invented so I think every country that writes it that way is correct and the Americans are not. So there!

My Japanese bank sends me reports with yyyymmdd file names, and the Japanese branch of Citibank (which I no longer use) sent me account reports with mmddyyyy file names. It was always a headache to get them into some sort of rational order. I think it is clear which of the two is superior.

I won’t start on the problem of the use of era-names on official documents in Japan (it’s now the 30th year of Heisei!).

Now if only there were calendar-expressible constants named cake. Or chocolate eclair. Or…

I’m surprised there are no tauists here. τ = 2π and is much less of a hassle to write. But there are quite a few physics variables that use τ so I personally won’t use it.