Bah Humbug...

For we Pi Day curmudgeons, Vi Hart comes through as usual:



(ohh, but, hey,  Happy Birthday to Albert Einstein... now that's something I can celebrate... with, a piece of pie perhaps!)

A Post, a Rant, and a Video

A few more links today in case you've missed them:

Evelyn Lamb continues the recent spate of commentary on pi with her take on pi and big (I mean B-I-I-I-G) numbers here:

http://blogs.scientificamerican.com/roots-of-unity/2013/04/17/big-numbers-are-big/

Wonderful rant from Grant Wiggins on the never-ending-wrangle over teaching high-school algebra:

http://grantwiggins.wordpress.com/2013/04/10/my-100th-post-so-why-not-bash-algebra/

And Keith Devlin weighs in, as well, on the teaching of algebra, in this 4-minute video:

Two for Tuesday

1) Here's a very good, informative commentary on Keith Devlin's math MOOC course (now at the 6-week point), from one of those enrolled in it; especially good read for anyone contemplating taking the course:

http://tinyurl.com/bqe9jck

(Keith is traveling right now, but it's probably close to time for him to weigh in as well with another update on the course at his MOOC blog.)

2) Overlapping a bit the Matt Springer piece I referenced a few days ago, here's another interesting post on the randomness of pi, this time from Huffington Post:

http://www.huffingtonpost.com/david-h-bailey/are-the-digits-of-pi-random_b_3085725.html

Speaking of pi, I'll leave you with this wonderful question wafting in your brain (...David Wees recently tweeted it as coming from his nephew, and I of course love its self-referential aspect):

"If Pi contains every possible sequence of numbers, does it contain itself?"

(...I think the answer is pretty clearly 'no,' but still a marvelous question from a nephew.)

Saturday Potpourri...

A few sundry items for your artful attention and possible perusal ;-):

1) Lance Fortnow, computer scientist and author of "The Golden Ticket," (which I reviewed a bit ago), all about P vs. NP, is Sol Lederman's latest podcast guest at Wild About Math:

http://wildaboutmath.com/2013/04/12/lance-fortnow-inspired-by-math-28/

2) A nice little primer on the nature of real numbers and pi from physicist Matt Springer here:

http://scienceblogs.com/builtonfacts/2013/04/12/everything-in-pi-maybe/

3) An interesting-looking list here of 24 video lectures in number theory:

http://www.infocobuild.com/education/learn-through-videos/mathematics/introduction-to-number-theory.html

4) Just a heads-up that E.O. Wilson is scheduled to be on NPR's Sunday "Weekend Edition" (tomorrow). I assume there will be some discussion of his recent much-debated commentary asserting that scientists need not know advanced mathematics to be successful.

5) Finally, a site I only recently learned of called "Ideas Roadshow" which looks interesting and includes this recent 5-minute clip by philosopher James R. Brown on Platonism in mathematics:

http://www.ideasroadshow.com/issues/james-robert-brown-2013-04-12

This and That…

Trouble In Mathland?…

Wow! I debated whether or not to cast attention on this matter, but it is moving around math circles and warrants an open-airing… a serious dispute over math education and harassment between university professors (aired by Jo Boaler of Stanford):

http://www.stanford.edu/~joboaler/
 (I guess math isn't always pretty... )

Keith Devlin wrote a (positive) bit about Boaler back in a 2010 posting (and she has plenty of other backers as well):

http://www.maa.org/devlin/devlin_06_10.html

Claims of her opponents are voiced in this pdf:

ftp://math.stanford.edu/pub/papers/milgram/combined-evaluations-version3.pdf

(I wouldn't want to get too mired in this dispute, which I suspect may get much worse before it gets better :-(, but will watch for any resolution that might eventually come about).

On to lighter material...

50 interesting facts about pi here:

http://facts.randomhistory.com/2009/07/03_pi.html

And in an interesting development, a TEDx talk from "Randy Powell" on so-called "vortex math" was finally yanked down as pure gibberish (how often does this happen?), though still available of course on YouTube:

http://www.youtube.com/watch?v=Yzfgq1zv8jg&feature=related

Finally, a little puzzle to end with (...think I grabbed this awhile ago from either Cliff Pickover or Ben Vitale but don't remember for sure!):

Only one 2-digit integer is both a square and a cube (n^2, p^3). What is it? And likewise there is only one 3-digit integer that is both a square and a cube. What is it??
....answer below
.
.
.
.
.
.
.
ANSWER:


64 (8^2 and 4^3) and 729 (27^2 and 9^3)


ADDENDUM: a good longer read now available on the Boaler controversy here (with many comments coming in):

http://tinyurl.com/9rrlw2v 

MacArthur Mathematician et.al.

(M. Chudnovsky via Wikipedia)

Not exactly synchrony but a recent bit of serendipity…

A couple days ago, bopping around the Web, I stumbled on a reference to Richard Preston's fascinating chapter from his 2008 book "Panic In Level 4" about the genius Chudnovsky brothers (Gregory and David) computing pi on a homemade computer in their Manhattan apartment (it's originally from a wonderful 1992 article Preston did for the New Yorker).
Such a great story I thought, even though a bit old, it might bear some ingredients for a blog post, and I went searching for my copy of Preston's book, only to find my own volume apparently dispatched to the used bookstore. I dropped the idea from my thoughts.

Then, the very next day, I looked over the names of the latest MacArthur Award winners… and there was one mathematician, 35-year-old "Maria Chudnovsky" among the lucky few -- hooray! gotta love seeing a mathematician get a MacArthur! (…frankly, I've not been too thrilled with some of the recipients in recent years :-(

Anyway, seemed like an odd coincidence to run into the "Chudnovsky" name twice in 2 days (perhaps though in Russian, "Chudnovsky" is like "Johnson" in America, I don't know ;-), so figured maybe a blogpost was in order after all (I've seen no mention of any connection between Maria and the brothers Gregory and David -- if someone knows of a relationship between them please inform us). Coincidentally, Gregory won a MacArthur himself back in 1981.

Anyways… here's part of the announcement from the MacArthur Foundation for Maria (including a nice video of her explaining some of her work):

http://www.macfound.org/fellows/862/

and another, brief older article on her as well:

http://www.popsci.com/scitech/article/2004-06/maria-chudnovsky

And below is a weblink to Preston's fine New Yorker piece on the brothers' pursuit of pi, still fascinating after all these years:

http://tinyurl.com/93kpj4l
(or, get pdf here: http://tinyurl.com/9ugo36d )

and here, a 10-min. NOVA video on them from PBS:

http://www.pbs.org/wgbh/nova/physics/chudnovsky-math.html

Pi = 2

A well-circulated paradox with a circle inscribed in a square results in π being equal to 4, but what I hadn't previously noticed was this similar James Tanton offering making pi equal to 2 (obviously considering these two paradoxes, pi must, on average, be equal to 3 ;-))

Pi & the Math of Buffon's Needle

Wasn't planning to do a post in honor of Pi Day (today), but may as well join the fray:
(video from Numberphile explaining the math behind pi and Buffon's needle... or in this case matches)

Are These Folks Humans or Cyborgs!?

Some people's brains are definitely wired very differently from mine....

When I first read of autistic savant Daniel Tammet's recitation of pi to over 22,500 decimals back in 2004, it seemed like a stunt beyond human comprehension, likely not to be surpassed in my lifetime… BOY, WAS I WRONG!!
It was a couple years later that I learned that Tammet's effort merely set a British and European record for pi recitation, but wasn't even close to the world record. As far back as 1981, an Indian had already recited pi to almost 32,000 digits, and a couple of Japanese blokes later greatly surpassed that endeavor. Then in 2005, a Chinese fellow, Chao Lu, would more than TRIPLE Tammet's puny ;-) performance, by reciting from memory, a phenomenal 67,890 digits of pi, and is still listed as the official record-holder by some accounts. Here's one listing of the world's top pi record-holders:

http://pi-world-ranking-list.com/lists/memo/

I'm not sure how these "official" designations are established though, because the current proclaimed record-holder is a former Japanese engineer, named Akira Haraguchi, who recited pi to 100,000 digits in 2006 (breaking his own prior record of almost 84,000):

http://www.foxnews.com/story/0,2933,217765,00.html

Simply UNNNreal! (...Having said that though, pi has now been computed to 10 trillion digits, so HEY Akira, ya gotta ways to go yet!)

...Now, if only I could remember where I left my car keys last night.

Obviously, Pi = 4

For any who have never seen it, an oldie-but-goodie puzzle today... simple proof that pi = 4 :

http://i.imgur.com/AzeYc.jpg

When I Was 13 I Was...

...trying to see the significance of Venn diagrams.

Some 13 yr.-olds (like cool kid Neil Bickford) busy themselves otherwise (perhaps calculating the first 458 million terms of pi....):

http://blog.wolfram.com/2011/09/15/from-pi-to-puzzles/
[link corrected]

"one quadrillion calculations per second"

For those who just can't get enough of pi (or otherwise have too much free time on their hands ;-):

http://tinyurl.com/3p5l839

(....the 60-trillionth binary digit of pi-squared calculated)

Tau Jam

Gotta luv effervescent Vi Hart (...though I suspect she drinks too much coffee)!  "Equalis Community Blog" brought my attention to another delicious (so to speak) video I'd missed from Vi, this time in honor of last week's Pi Day, but celebrating Tau instead --- if you don't know about Tau (the equivalent of 2π) you can check it out here:

http://tauday.com/

But I'd go ahead and view Vi's effort first:

Huhhh, WHOAAAA!!!

From the "learn something new everyday" category:

I'd always thought that autistic savant Daniel Tammet's recitation of pi (from memory) to 22,514 digits in 2004 was an unbreakable (and unfathomable) world record. How WRONG I've been! Turns out that was only a puny European record...

Hat tip to "SquareCircleZ" blog for enlightening me that a prior 1995 world record, set by a 21-year-old Japanese student at 42,195 digits, was well surpassed in 2005 by a Japanese mental health counselor at 83,431 digits!!!! (Forget pi, one of these gents should be working on the Riemann Hypothesis! :-):

http://news.bbc.co.uk/2/hi/asia-pacific/4644103.stm

Holy Geekfest Batman!, I can barely remember my social security number... :-(

Celebrate, Celebrate!

Monday is Pi Day, 3/14, in honor of possibly the world's most famous number, so go ahead and check it out here (...it also happens to be, somehow fittingly, Albert Einstein's birthday!):

http://www.piday.org/


Over the years a lot of folks, in tribute to pi, have written parodies to Don McLean's classic "American Pie." As a product of the 60's/70's though I have to demur that Don McLean's own version still remains the best!! So, for all the baby boomers out there, a little nostalgia ;-):

π = 4... NOT!

Fun with pi today....

From Equalis Community blog, discussion of a paradox indicating that π = 4, and why it ain't so:

http://www.equalis.com/members/blog_view.asp?id=565749&post=121290

"The Tau Manifesto"

Mark Chu-Carroll at his blog, "Good Math, Bad Math," often posts examples of mathematical 'crackpottery' that come his way, but recently posted about an argument for why everyone's favorite number π, should really be substituted with another value tau, τ, the equivalent of 2π, and why this would all make sense in so many ways (tau is based on the radius of a circle, instead of the diameter-basis for pi). And yes, it's a serious argument:

http://tauday.com/

Many agree with the logic and reasoning of the assertions in favor of 'tau,' but... well... changing centuries of routine use of pi (and making obsolete all those 'I Love π ' t-shirts) , is of course another matter altogether.

Some Miscellany For Wednesday

Another look at the foundations of mathematics in upcoming book:

http://tinyurl.com/33ylyvp

If you can't get enough of Pi:

http://facts.randomhistory.com/2009/07/03_pi.html

James Tanton's newly-active Twitter feed here:

http://twitter.com/#!/jamestanton

Pi: The Number That Keeps On Giving....

Ever get the feeling that perhaps some people just have too much free time on their hands ;-)....

In news, that we've all been hungry for, it's been announced that the two-quadrillionth digit of pi has been determined... in binary... to be a zero!:

http://www.bbc.co.uk/news/technology-11313194

It's still the case that only a mere 2.7 trillion consecutive digits of pi are known, but powerful cloud computer techniques are now able to find specific digits much farther out. But more importantly... can these techniques help me find my car keys in the morning???

Seriously though, congratulations to those involved!

Daniel Tammet Has His Work Cut Out For Him Now ;-)

Japanese and US computer scientists claim to have calculated Pi to five trillion decimal places... just a few trillion more than the previous record! (...but I'll save some space here by not typing it out for you):

http://pda.physorg.com/trilliondecimal-decimalplaces-computer_news200209829.html

[Daniel Tammet, BTW, is the autistic savant famous for having recited Pi accurately from memory to over 22,500 digits back in 2004.]