Archive for Numbers

Happy π Day from Nine Kinds of Pie

π Day is upon us once again!  Here are 3.14 pieces of Pi (as it were).

1. The π sculpture in Seattle, Washington.

Pi sculpture, Seattle, Washington

Photo by Niall Kennedy.

2. π to 1000 decimal places

3.1415926535897932384626433832795028841971693993751058209749445923078

16406286208998628034825342117067982148086513282306647093844609550582

23172535940812848111745028410270193852110555964462294895493038196442

88109756659334461284756482337867831652712019091456485669234603486104

54326648213393607260249141273724587006606315588174881520920962829254

09171536436789259036001133053054882046652138414695194151160943305727

03657595919530921861173819326117931051185480744623799627495673518857

52724891227938183011949129833673362440656643086021394946395224737190

70217986094370277053921717629317675238467481846766940513200056812714

52635608277857713427577896091736371787214684409012249534301465495853

71050792279689258923542019956112129021960864034418159813629774771309

96051870721134999999837297804995105973173281609631859502445945534690

83026425223082533446850352619311881710100031378387528865875332083814

20617177669147303598253490428755468731159562863882353787593751957781

8577805321712268066130019278766111959092164201989

This website lists π out to its one millionth digit. So does this one.

3. My childhood obsession with this number.

I have never cared a great deal about the ratio of a circle’s circumference to its diameter.  But, when I was a child, I did memorize π out to its tenth decimal point. I also wrote it out on a piece of paper out to its hundredth decimal point — an item I discovered a couple of years ago when cleaning out my childhood archive (then stored in boxes in my mother’s basement). Why write it out to the hundredth digit?  Perhaps I planned to memorize the number all the way out to that decimal?

Most likely, its novelty captivated me.  I loved paging through the Guinness Book of World Records, and even bought a new edition of the book each year.  There, you could learn about Chang and Eng Bunker, or the longest word (that isn’t a technical term or proper noun): floccinaucinihilipilification, which (in case you were wondering) is the act of estimating something worthless.  π is not worthless, but my attraction to it derives more from its oddity than its utility.

The sarcastic among you might observe that an affection for arcane information is a fairly good description of my profession — college professor. And you wouldn’t be entirely wrong. But you would be belittling the fact that knowledge is worth pursuing for its own sake. Knowledge has no obligation to be useful. Or, to put this another way, do not be discouraged if its purpose may initially elude you.  You never know when knowledge might come in handy, or what ideas it might generate.

0.14.  Two Previous Posts on π

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Nine Kinds of Pie

Happy Pi Day!  In recognition of 3.14 (today) and this blog’s Pi pie avatar (logo?), here are Nine Kinds of Pie (loosely defined).

Pi1. The ratio of a circle’s circumference to its diameter: 3.1415926535.  When I was a kid, I memorized the number out to its tenth decimal point. On a long strip of paper, I also wrote the number out to about 100 decimal points. Perhaps I thought that learning this irrational number would grant me some greater insight. Or, possibly, I was intrigued by the fact that this simple ratio would be represented by such an unwieldy and unending number. I’m not sure. But I still have a fondness for Pi (and pie!). For the truly obsessed, here is Pi out to 100,000 decimal points. Here’s Pi Day’s “Learn About Pi” page, the Joy of Pi’s “Pi Facts,” and Wikipedia’s essay.

Pi: one hundred digits


2. Pi was also important to Crockett Johnson. In his later years, he worked on the mathematical conundrum of squaring the circle — a problem that also intrigued mathematician and children’s author Lewis Carroll, a century earlier. Johnson even published his own original theorem on the subject.

Crockett Johnson, from the Mathematical Gazette (1970)
Crockett Johnson, algebraic proof from the Mathematical Gazette (1970)

He moved towards this answer, visually. He literally worked out the problem via his paintings, creating many variations on the idea, and ultimately arriving at Squared Circle (1968).

Crockett Johnson, Squared Circle (1968)

Then, to get the algebraic notation correct, he corresponded with mathematicians, who helped him express his idea in the less visual medium of the formula. It was published in the Mathematical Gazette in 1970.


3. As readers of children’s literature know, this blog takes its name from a scene in Johnson’s Harold and the Purple Crayon (1955), in which the title character “laid out a nice simple picnic lunch.”

Crockett Johnson, Harold and the Purple Crayon (1955): "There was nothing but pie."

I love the way Johnson’s tone both embraces Harold’s matter-of-fact tone and registers amusement at this claim. On the one hand, the third person narrator (via a literary technique known as free indirect discourse) tells us what Harold is thinking: our narrator is so closely aligned with Harold’s point of view that one could easily swap the pronouns and Harold’s name for “I.” These are Harold’s thoughts. On the other hand, they’re not entirely Harold’s thoughts. Johnson’s deadpan delivery of these lines also underscores the mild absurdity of having nine favorite kinds of pie. That is, there’s also an awareness here that Harold lacks — specifically, that “nine kinds of pie that Harold liked best” is  funny.


4. Or is it? This somewhat baffling pie chart lists Americans’ 10 favorite types of pie.

Pie chart of Americans' favorite types of pie

It’s somewhat baffling because the percentages don’t add up to 100 — which is the point of using a pie chart. The circle represents 100%, and then each slice some lesser percentage. But this chart doesn’t. As the chart’s caption explains, the total “adds up to more than 100 per cent because people were asked to rank their three favorite types of pie.” And that still doesn’t make the above chart any more illuminating — though it is pretty to look at.


5. Pies are among those foods that come in both sweet and savory varieties. When I think of pie, my thoughts drift to the sweet (apple, peach, pecan, blueberry), but there are are also savory pies (meat pie, chicken pot pie, potato pie, pizza pie). The Oxford English Dictionary, which finds the oldest use of the word “pie” (then spelled “pye”) in 1304, offers the following as its  first definition:

A baked dish of fruit, meat, fish, or vegetables, covered with pastry (or a similar substance) and freq. also having a base and sides of pastry. Also (chiefly N. Amer.): a baked open pastry case filled with fruit; a tart or flan.


6. Care for some Amblongus pie? Since this is (often) a children’s literature blog, here’s a recipe from Edward Lear’s “Nonsense Cookery” (which appears in his Nonsense Songs, Stories, Botany, and Alphabets, 1871).

TO MAKE AN AMBLONGUS PIE

Take 4 pounds (say 4 1/2 pounds) of fresh Amblongusses, and put them in a small pipkin.

Cover them with water and boil them for 8 hours incessantly, after which add 2 pints of new milk, and proceed to boil for 4 hours more.

When you have ascertained that the Amblongusses are quite soft, take them out and place them in a wide pan, taking care to shake them well previously.

Grate some nutmeg over the surface, and cover them carefully with powdered gingerbread, curry-powder, and a sufficient quantity of Cayenne pepper.

Remove the pan into the next room, and place it on the floor. Bring it back again, and let it simmer for three-quarters of an hour. Shake the pan violently till all the Amblongusses have become a pale purple colour.

Then, having prepared a paste, insert the whole carefully, adding at the same time a small pigeon, 2 slices of beef, 4 cauliflowers, and any number of oysters.

Watch patiently till the crust begins to rise, and add a pinch of salt from time to time.

Serve up in a clean dish, and throw the whole out of the window as fast as possible.

For any readers unfamiliar with Lear’s nonsense works,… you’re in for a treat even tastier than amblongus pie and gosky patties. Go read ’em!


7. John Cage and Lois Long’s Mud Book (written 1950s, published 1983) offers a recipe for mud pie — and yes, this is John Cage, the composer.

John Cage and Lois Long, Mud Book (1983)

 

John Cage and Lois Long, Mud Book (1983)

 

John Cage and Lois Long, Mud Book (1983)

 

John Cage and Lois Long, Mud Book (1983)

As Lane Smith and Bob Shea write in their post on Mud Book (and my source for these images), “Instructions any child can follow with ingredients easy to obtain. Notably, dirt, rocks, water, dirt and more dirt. But remember, mud pies are to make and to look at. Not to eat.”


8. Michael John Blake’s “What pi sounds like” is my favorite musical interpretation of the number. (It’s also literally a “musical number.” Get it?)

Many others have composed music inspired by Pi. Lars Erikson — composer of the Pi Symphony — even sued Michael John Blake (composer of the above piece), alleging plagiarism. Erikson lost.

If you like it (and if you don’t), you can  buy Michael John Blake’s “What pi sounds like” via iTunes.


9. One could make a long list of pie-themed music, too. The earliest one that comes to mind is “Song of Sixpence” (18th century): “Sing a song of sixpence, / pocket full of rye. / Four and twenty blackbirds / baked in a pie.” There’s A. A. Milne’s “Cottleston Pie,” performed here by Rowlf the Dog on the first season of The Muppet Show (1976).

According to an informal and completely unscientific survey of the “pie” songs in my iTunes, pies usually function metaphorically in music. Yes, there are “The Worst Pies in London” (from Sondheim’s Sweeney Todd) and Zoe Lewis’s “Pies for the Public” (from Sheep), but you’re more likely to encounter Don McLean’s “American Pie” (1971), Jay & the Techniques’ “Apple, Peaches, Pumpkin Pie” (1967), the Beatles’ “Honey Pie” (from The Beatles [White Album], 1968), David Wilcox’s “Wildberry Pie” (1991), Death Lurks’ “Happiness Pie” (from The Kids in the Hall soundtrack, 1996), or Louis Jordan and Ella Fitzgerald’s “Patootie Pie” (1946).


And what better way to express one’s appreciation for Pi and pie than by baking a Pi pie?

Pi pie

If you want to make one, the Nerdista has a recipe for her Pi pie (pictured below).

Nerdista's Pi Pineapple Pie

Happy Pi Day! Let’s have some pie. And Pi, of course.

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Happy π Day from Crockett Johnson

Nine kinds of pie (from Crockett Johnson's Harold and the Purple Crayon)This isn’t the only kind of “pie” that Crockett Johnson was interested in.  In addition to “all nine kinds of pie that Harold likes best,” Johnson also drew inspiration from π (3.14159265…) — the ratio of a circle’s circumference to its diameter.

In early 1968, he began the project of “squaring the circle,” constructing a square with the same area as a circle — but using only a straight-edge and a compass to do so.  This is impossible, but he was either unaware of this fact or undeterred by it.  Not a trained mathematician, Johnson worked his way towards the answer visually.  He painted solutions, testing different theories on his canvas (which was actually mortarboard — canvas intimidated him).

By the middle of the year, he had arrived at a solution:

Crockett Johnson, Squared Circle (1968)

He painted two versions of this.  The other can be found at the Smithsonian’s on-line exhibit, Mathematical Paintings of Crockett Johnson.  I recommend you visit its site for a more complete explanation of the mathematics behind the painting.

Johnson next wrote up an algebraic formula, and sought the opinion of professional mathematicians.  Finally, in 1970, the Mathematical Gazette published his first mathematical theorem, “A geometrical look at √π”:

Crockett Johnson, from the Mathematical Gazette (1970)
Crockett Johnson, algebraic proof from the Mathematical Gazette (1970)

Johnson would publish his second original contribution to the field of mathematics in 1975, just prior to his death.

Learn more:

Other examples of Crockett Johnson’s work (from this blog):

 

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Twelve is number 1!

Robert Krulwich has many ideas on how to celebrate 12/12 (today), including paying a visit to the Dozenal Society of America’s website.  Here are two more contributions to the “12” party.  First, it’s “Rocks Number 12,” a 2-minute animated film that aired on Sesame Street in the early 1970s.  This is my first memory of the number 12, and it’s the primary reason that (when I was growing up) 12 was my favorite number.

Indeed, if I were asked today to name a favorite number, I would still choose the number 12.  Of course, this wasn’t the only moment that Sesame Street invited viewers to spend time with the number 12.  As you may recall, another 12-themed animated short was “The Ladybugs’ Picnic”:

So, was Sesame Street was covertly advancing a dozenist agenda?  Is Public Broadcasting propagandizing for mathematical radicals?  If I ask enough ludicrous hypothetical questions, will concerned citizens argue for a full audit of Sesame Street‘s YouTube channel?  Or have you stopped reading this in order that you may scroll back up and play the happy videos?  I know I have.  I stopped reading this, oh, a dozen sentences ago.

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