Friday Puzzle

Yeah, I'm a sucker for basic (but clever) geometry puzzles, so here's another one from "Futility Closet" from a month+ ago:

http://www.futilitycloset.com/2011/08/17/rest-stop/

(click where indicated in the posting to see the surprisingly simple answer)

New Aczel Book

The always-interesting Amir Aczel has a new volume out that should be of interest, "A Strange Wilderness: The Lives of the Great Mathematicians":

http://www.amazon.com/Strange-Wilderness-Lives-Great-Mathematicians/dp/1402785844

Here's the blurb from Publisher's Weekly:

http://www.publishersweekly.com/978-1-4027-8584-9

"Math In the Real World"

"Home School Math" has put up a nice page of resource links (entitled "Online Math Resources For Math in the Real World") for math teachers/homeschoolers/students or just math fans:

http://www.homeschoolmath.net/online/real_life_math.php

Popcorn Time... Math Movie

A movie for math buffs! Hooray!! "Julia Robinson and Hilbert's Tenth Problem," a 1 hour movie about... Julia Robinson (1 of the major female mathematicians of her day) and Hilbert's 10th problem (dealing with the algorithmic solvability of Diophantine equations) will be playing in various locales in October. See here for possible air dates in your area:

http://www.zalafilms.com/films/jrairdates.html

Wikipedia entry for Hilbert's 10th problem here:

http://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem

entry for Julia Robinson here:

http://en.wikipedia.org/wiki/Julia_Robinson

And here's the movie trailer to whet your appetite:




(David Hilbert image via Wikimedia Commons)

Gödel Simplified... sort of

I got a big kick out of this 1994 1-page (pdf) explanation of Gödel's Second Incompleteness Theorem from George Boolos, all in single-syllable words (literally)... pretty impressive!:

http://bit.ly/bWrBqz

Geometry Lovers...

I only recently discovered this great site with a great many cool geometry problems (mostly high school level):

http://gogeometry.com/problem/index.html

the more general home page for the site here:

http://gogeometry.com/

Friday Puzzle

For a Friday puzzle I'll just link you to this one from Presh Talwalkar from several weeks ago (...another geometry-oriented puzzle, involving string-cutting; with the answer included in the comments to Presh's post):

http://mindyourdecisions.com/blog/2011/08/29/geometry-puzzle-string-cutting-game/

(Math) Teaching and Twitter

Mr. Honner recently noted how much he now uses Twitter for ideas and connections to assist his math teaching activities. I suspect most of you already use Twitter, but if not, he offers a straightforward basic introduction to its use and benefits here:

http://mrhonner.com/2011/09/18/math-teachers-and-twitter/

He includes a list of some of the mathematically-inclined Twitter feeds he follows for his purposes. And if you want a much longer, broader list of math-related Tweeters you can check out this list from Listorius:

http://listorious.com/search/people?q=math&search=Search

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]

"How Algorithms Shape Our World"

A fine TEDTalk from Kevin Slavin on how mathematics rules the world, with or without human supervision!

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Collatz Fans

If you're really into the Collatz (3n+1) Conjecture nice new long piece on it here:

http://home.graysoncable.com/dkcox/

Moebius Noodles

The internet is the greatest distributor of information and potential educator in human history. And now Maria Droujkova has started the "Moebius Noodles Project" as an open access math education opportunity for youngsters, and even babies. Word has been spreading in math circles about the endeavor. If you're unaware of it, read more about it at these links and contribute if you can -- math education, especially for children, has never been more important than it is today:

http://www.naturalmath.com/blog/moebius-noodles-fundraiser/

http://www.naturalmath.com/blog/

Oldie-but-Goodie

I've used this old YouTube version (from the movie "Labyrinth") of one of the "liar paradoxes" before, but it's so much fun, worth showing again:



(If you need help working through the logic involved you can try this page: http://dabbycool.com/nooblingsnest/?p=100 )

Mathematics and the Aha! Moment

A post on mathematical insight from Peter Ash with a nice example from geometry:


http://tinyurl.com/44n2m7d

The Arbitrariness of Statistical Significance

Partly in response to some of the articles I've cited here earlier, physicist Chad Orzel writes this cogent worthwhile piece on the "arbitrariness" of statistical significance:

http://tinyurl.com/5v5raef

(...lots of interesting followup points/discussion in the comments section as well... be sure to peruse)

Daniel Lewin 1970 - 2001

KW Regan writes this tribute to mathematician/polynomial researcher, computer scientist, Akamai Technologies founder... and, 9/11 victim Daniel Lewin:

http://rjlipton.wordpress.com/2011/09/12/911-and-the-web/

Problems In Academia...

According to this piece approximately 50% of published studies from academic labs are not replicable. Not too surprising given the complexity of the variables involved, but not often acknowledged... (and how poor would the rate be among NON-published studies, which are the vast majority?):

http://marginalrevolution.com/marginalrevolution/2011/09/how-good-is-published-academic-research.html

In a slightly related matter, Ben Goldacre points to a widespread statistical error, dealing with "the difference in differences," that is commonplace in published (neuroscience) studies:

http://www.guardian.co.uk/commentisfree/2011/sep/09/bad-science-research-error

"Stay Hungry, Stay Foolish"

Image via Wikipedia

No math post today... just more of a Sunday sermon, courtesy of Steve Jobs, an individual of heroic proportions to many. Actually, it's courtesy of the Twittersphere where I found the link to this wonderful commencement speech Jobs gave at Stanford in 2005. No reason to wait 'til the end of a school-year though to pass such nuggets around:

http://news.stanford.edu/news/2005/june15/jobs-061505.html

"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma — which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary."

...And on a separate note, can't help but in some way commemorate the incomprehensible tragedy of 10 years ago today -- Art Garfunkel sings this classic S&G in Central Park:

15,000 Pages of Calculations...

Michael Aschbacher of Caltech will be receiving the $75,000 Rolf Schock Prize for his part, among dozens of mathematicians who contributed, in the solution to the largest mathematical proof EVUH(!) involving the "Classification Theorem of Finite Simple Groups" (also, simply and appropriately known as "The Enormous Theorem").
Read all about it:

http://www.newscientist.com/article/dn20893-prize-awarded-for-largest-mathematical-proof.html

Of Squares and Circles, Pegs and Holes

Another simple Friday puzzle adapted from Richard Wiseman this week (just by guessing you have 50% chance of getting it right):

"Which is a better fit (i.e., results in less wasted space), a square peg in a round hole or a round peg in a square hole?"

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.answer:  a round peg fits into a square hole better than a square peg in a round hole

if you need an explanation you can view the answers posted at Wiseman's site:

http://richardwiseman.wordpress.com/2011/08/15/answer-to-the-friday-puzzle-117/

Testing 1 2 3

In the below post "Mr Honner" draws attention to a rather important consideration when it comes to the standardized math testing that is now prevalent for evaluating student success: Are the tests ANY GOOD?

http://mrhonner.com/2011/09/05/are-these-tests-any-good/

Noting that such tests are now used to evaluate not just students, but teachers and schools as well, he points out that mathematical errors, poor wording, and poor representation of subject matter, are more common than they ought be for quality, meaningful testing.

Fermat's Last Theorem (VIDEO)

"Math-Fail" directs readers to view this video on Andrew Wiles and Fermat's Last Theorem. It is indeed excellent and enthralling (45 mins. long). I too encourage all math-lovers who have never seen it to find the time to view it. It very well depicts the love, devotion, and elation a human being can experience toward a subject that so many others view as merely dry and tedious:



(...and what I really like is Wiles' workdesk, which actually makes mine seem almost orderly! ;-))

Statistical Puzzle

Toss a fair coin. Is the average number of coin tosses required to get a HTH pattern greater than, less than, or the same as, the number of tosses required to get a HTT pattern?

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answer: greater than (on ave. taking 10 tosses to get HTH, and only 8 to get HTT)

See Peter Donnelly's TED talk if you need an explanation: http://bit.ly/qYlgHi