Hyperbolic Space et.al. and Vi Hart

Interesting interview, from New Scientist, with the creative Vi Hart here:

http://www.newscientist.com/blogs/culturelab/2011/03/mathematical-artist-why-hyperbolic-space-is-awesome.html

Incredible Kid!

WOW! 12-year-old autistic math/physics prodigy reworking Einstein here:

http://tinyurl.com/4oa599v

April Come She Will

Why am I embedding an old Paul Simon song into a math blog post?... 'cuz I'll use any excuse I can to play old Simon & Garfunkel tunes, AND because April is officially "Mathematics Awareness Month" --- it has been since 1986, when President Ronald Reagan declared it so. Each year a different theme is chosen, and this year the theme is "Unraveling Complex Systems." More here:

http://www.mathaware.org/mam/2011/announcement/

And a Facebook page devoted to Mathematics Awareness Month (or MAM) is here:

http://tinyurl.com/4q99tmp

Here are the prior dozen years' themes:

2010 - Mathematics and Sports
2009 - Mathematics and Climate
2008 - Math and Voting
2007 - Mathematics and the Brain
2006 - Mathematics and Internet Security
2005 - Mathematics and the Cosmos
2004 - The Mathematics of Networks
2003 - Mathematics and Art
2002 - Mathematics and the Genome
2001 - Mathematics and the Ocean
2000 - Math Spans All Dimensions
1999 - Mathematics and Biology

So put mathematics front-and-center... April come, she will be!

Proving Morley's Theorem

Image via Wikipedia

 Triangles, circles, and trisections, oh my!....

Hat tip to Pat's Blog for leading me to this fascinating proof of "Morley's Theorem" over at a physics blog:

http://commonsensequantum.blogspot.com/2011/03/morley-triangle-derived-from-tripling.html

"Morley's theorem" states that the trisectors of the three angles of any triangle will always intersect to form an equilateral triangle.

AHHH, Geometry lives and breathes!!

Science, Measurement, and Learning

Many of you will have read this story somewhere before, about a student in a physics class, answering a question (I first read a version of it back in the 1970's). I just discovered this telling of it on the ever-wonderful "Cut-the-knot" site, and it's always worth introducing to more folks. (also, it ties in directly to the post I put up a week ago also relating to the assessment of student achievement):

http://www.cut-the-knot.org/manifesto/thinking.shtml

Factoid...

A recent "Futility Closet" post noted that:

the polynomial x^2 – 2999x + 2248541 produces 80 primes from x = 1460 to 1539

...more on the topic here:

http://www.scribd.com/doc/38223320/Computational-Data-On-x-2-%E2%80%93-2999x-2248541

Fractal This! :-)

A joke I saw somewhere on the Web awhile back (I'd give credit if I knew where it came from):

Do you know what the "B" in Benoit B. Mandelbrot stands for?

answer: "Benoit B. Mandelbrot"....

...if you don't get it right away, think about it.

Able John Milnor

Fields Medals may be the most well-known mathematical prizes, though they are limited to recipients 40 yrs-old and younger. The Abel Prize in mathematics, really comes closer to a Nobel Prize in the sciences. And this year it has been awarded to 80-year-old John Milnor for a lifetime of contributions (he is also an earlier Fields recipient):

http://www.nature.com/news/2011/110323/full/news.2011.182.html

For a more technical take on Milnor and the award see Tim Gowers post:

http://gowers.wordpress.com/2011/03/23/milnor-wins-2011-abel-prize/

Math and Gender

A recent study published in "Child Development" indicates that we haven't made a lot of progress in the 'math is for boys' stereotype that so often steers girls away from math at a young age:

http://tinyurl.com/4tt9lpn

From the article:

“Our results show that cultural stereotypes about math are absorbed strikingly early in development, prior to ages at which there are gender differences in math achievement,” says co-author Andrew Meltzoff, a professor of psychology.

...we still have a lot of work to do (...and I can't help but think that the Web will be a powerful tool in bringing an end to the stereotype).

Triangle Navels

Alex Bellos has another interesting post, this time on 'triangle centres'... you likely know 3 or 4 of them, but would you believe there are an infinite number! Who knew!?.... turns out a math guy in Indiana knew:

http://alexbellos.com/?p=1527

How To Assess Students???

In some ways this is an age-old question, but that doesn't stop it from being interesting when raised anew: in the below post, "Irrational Cube" blog essentially asks if the assessment of student abilities (in math) can really be valid if that assessment seems dependent on the format of the material being used:

http://irrationalcube.wordpress.com/2011/03/11/assessment-limits-the-farmers-fence/

I think commenter #2 has it largely right in his/her response, though there may still be room for other thoughts/ideas.

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:

Speaking of March Madness...

'Hot hands' in basketball... and statistics. . . .

Below, a statistical post from Williams College that seems at least slightly appropriate to the week coming up:

http://blogs.williams.edu/math/2011/01/03/the-hot-hand/

(includes a "game" teachers can employ in their own classrooms)

"Picking Holes In Mathematics"

If you're interested in the underpinnings of mathematics, an interesting article from plus.maths.org here, entitled "Picking Holes In Mathematics":

http://plus.maths.org/content/picking-holes-mathematics

Early on it starts off in this vein:

"The logician Kurt Gödel proved in the 1930s that if you set out proper rules for mathematics, excluding leaps of faith or intuition as admissible moves, you lose the ability to decide whether certain statements are true or false. And this isn't because you chose the wrong rules: for any set of rules, as long as they're strong enough to make sense of whole number arithmetic, there will be statements you can't prove or refute.

"This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite artificial and didn't touch on ordinary everyday mathematics."

...and then it goes on to recount some of the work of Harvey Friedman of Ohio State University in the arena of Gödel incompleteness.

Quote... Unquote

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that "laws of nature" exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

-- Eugene P. Wigner

"I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe."

-- Isaac Asimov

Number Fans, Student Geeks, Math-Frolickers...

...Lend me your wallets!

Sorry to be so commercial, but Spring's around the corner, so check out all the t-shirt designs/mugs etc. available at my Zazzle store here (order for yourself, significant others, or for conference attendees!):

http://www.zazzle.com/sheckyr/gifts?ps=45#products

Some of the current designs:

           "Prime Numbers ROCK!"

           "Math Is Infinitely Cool!"

           "Euler, Gauss, Hilbert, Riemann ...The Fab Four"

 "Like Math...? Let's Frolic!!"

           "Show Me Your Algorithm and I'll Show You Mine"

"Viva La Math!"

"WWMGT (What would Martin Gardner think?)"

"Math Sizzzles  ...and so do i "

"Revenge of the Math Geeks"

           "Math Is Sixy!"

 "M.I.B.T.  (Math iz a bee-eautiful thang!)"

 "1,2,3,4,5... Yo! What's your Erdos Number?"

           "Science Buff or... Buff Scientist!"

 "Blogito Ergo Sum (I blog therefore I am!)"

            ...and more!

--- please note that I've generally posted the most inexpensive styles Zazzle offers to hold costs down, but you can easily choose to order any design in a different color/style (than the one shown) and pay slightly more.

...and if you buy all these up... hey, we'll make MORE! ;-)

Math et.al. Conference

The below week-long conference, on "semiotics, cognitive science, and mathematics," beginning today in Canada, looks interesting to me (although I'm only familiar with a couple of the names participating):

http://www.fields.utoronto.ca/programs/scientific/10-11/semiotics/

If anyone in attendance is regularly blogging or tweeting about the conference I'd be interested to know of it.

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 ;-):

"Global One-World Classroom"

Chances are, if you read my blog, you already read Sol's "Wild About Math" blog, but if by some quirk you've missed it, he just posted this recent interesting 20-min. TED talk from Salman Khan (founder of Khan Academy, which I also hope you're already familiar with) on the future of math, and other, education:





(...makes me jealous of youngsters being educated today versus my stodgy learning days)

Of Kuhn and Pythagorus

Errol Morris at the NY Times has been running a (5-part) series centered around philosopher Thomas Kuhn (of "paradigm-shift" fame). Part 3, is just out, and if historical (or, in this case, ancient) mathematics interests you, you may find his discussion of the Pythagoreans, "incommensurability," and irrationality of √2, quite fascinating --- the piece is long (and the extensive footnotes also worth reading), so only link to it when you have some time to sit and read:

http://opinionator.blogs.nytimes.com/2011/03/08/the-ashtray-hippasus-of-metapontum-part-3/

The first two parts of this engaging series are below:

http://opinionator.blogs.nytimes.com/2011/03/06/the-ashtray-the-ultimatum-part-1/

http://opinionator.blogs.nytimes.com/2011/03/07/the-ashtray-shifting-paradigms-part-2/

(For those of you who are Thomas Kuhn fans, I'll warn you that Morris is not.)

Mathematics Simmering

Yesterday, a post from Joselle at "Mathematics Rising" that very much appeals to my philosophical (or cognitive psychology) side:

http://mathrising.com/?p=462

...contains several wonderful quotes in regard to the nature of mathematics and its relationship to human cognition.

Rock-Paper-Scissors Fans

On the heels of IBM's Watson's victory on 'Jeopardy,' you can play "Rock-Paper-Scissors" against a computer online via this NY Times piece:

http://tinyurl.com/6fk9us8

Have at it! (...do try to get some work done today as well, though)

Of Wheels and Circles and Points, Oh My!

Steve Colyer, at "Multiplication By Infinity" blog, tackles Aristotle's classic "Wheel paradox" here:

http://tetrahedral.blogspot.com/2011/03/aristotles-wheel-paradox.html

The above image-in-motion makes the paradox especially powerful (making two clearly different circumference sizes seem equal).

In a brief search, I couldn't find a really good explanation of the paradox for the layman, on typical math sites. Bryan Bunch treats it as well as any in the first chapter of his old volume "Mathematical Fallacies and Paradoxes," which is available online here:

http://tinyurl.com/4j8q7e6

The explanation lies in the need to follow the path of a single point on a circumference as it moves from point A to point B, following its actual curved or cycloidal path and NOT a straight line, in order to understand the relative unwinding of the two circumferences.
The paradox also touches upon the topic of infinity and cardinality (and their fuzziness in our mind!).

Some of the old paradoxes are still among the best!

There Is No Title For This Post

This is the first sentence of the post titled, 'There is no title for this post.' This appears to be the sentence that follows sentence #1 of that post. This is the sentence following the previous sentence, but preceding the next sentence. This is the next sentence... or is it? Apparently this is sentence #5. This is the sentence you just finished reading. The last sentence of this post will come at the end. Thus, this is NOT the last sentence of this post. It is untrue that the prior sentence was false. This sentence begins with the word "this," followed by the word "sentence," followed by the word "begins," followed by the word "with," followed by the word "the," followed by the word "word," ...AND also ends with the word "word." And this is the sentence that informs you that the very next sentence is the final sentence of this post. This is the last sentence of the post, but why oh why does it end with a question-mark?

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

New Devlin Book

New book out from Keith Devlin dealing with math education and video games:

http://tinyurl.com/66yrpyz

I generally like Devlin's popular writings, but wouldn't want to pre-judge this one before actually seeing it, as it's potentially a controversial topic. But here's his latest online column on the same subject:

http://www.maa.org/devlin/devlin_03_11.html