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Friday, December 31, 2010

Monday, December 27, 2010

Reindeer Problem From Wiseman

Richard Wiseman's prior-Friday Christmas problem here:

http://tinyurl.com/2bqgj2b (has problem & answer)

If you want to read the problem without the answer being immediately given go here (and get a bonus video in addition, as well):

http://tinyurl.com/2fbgtlp

The 'Surprise' of Mathematical Connections

Another interesting post from RJ Lipton here:

http://rjlipton.wordpress.com/2010/12/26/unexpected-connections-in-math

This time on the "beauty and power" of "unexpected connections" in mathematics, where findings or knowledge from areas that seem to have little overlap, are conjoined to produce yet newly useful knowledge or proof. This can happen in other areas of science, but is an especially integral underlying part of modern mathematics with its complex, almost unwieldy proofs, going forward.
The post starts off with reference to illustrious mathematician and economics Nobel-Prize winner John Nash (famous to lay folks from the book and movie "A Beautiful Mind"), before delving into some more abstract and technical discussion.
Mathematics, full of surprise and beauty, signifying much.

Tuesday, December 21, 2010

Just A Couple of Book Notes...

The new Reuben Hersh/Vera John-Steiner book, "Loving and Hating Mathematics: Challenging the Myths of Mathematical Life" should be available in stores very shortly:

http://www.amazon.com/Loving-Hating-Mathematics-Challenging-Mathematical/dp/0691142475

[Addendum: just received a review copy of the above volume in mail so will have more to say about it perhaps sometime after the Holidays.]

And a rough draft (pdf download) of yet another book for lay people on the Riemann Hypothesis is available here (Barry Mazur co-author):

http://wstein.org/rh/

Sunday, December 19, 2010

Fractals From NOVA

Hat tip to "Grey Matters" for directing me to this 2008 hour-long PBS 'NOVA' episode on fractals, entitled "Hunting the Hidden Dimension":

http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html

Friday, December 17, 2010

Links and Gifts

Sol's usual array of interesting math links for this week at Equalis Community Blog here:

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

(if you don't find at least one link there interesting to you, better check to see if you still have a pulse ;-))

And if you haven't yet finished holiday-shopping for all your math-geeky friends, Denise had several suggestions here:

http://letsplaymath.net/2009/12/22/have-a-mathy-christmas/

Google's Word Corpus

growth in interest in prime numbers and number theory:

http://tinyurl.com/22juwgm

growth in interest in arithmetic, not so much:

http://tinyurl.com/25km6aq

Wednesday, December 15, 2010

Timekeeping For Geeks ;-)

I don't comprehend all these hourly designations, but some of you probably will (...worth a chuckle):

http://www.beaverdam.k12.wi.us/bd/content/mathclock%20withnumbers.jpg

...and here a prime number watch:

http://tinyurl.com/2uop37u 

And finally a watch based on, of all things, the Sierpinski Triangle:

http://tinyurl.com/2fqolo5


(Perhaps some people just have too much time on their hands! ;-)

Tuesday, December 14, 2010

Poincare and the Continuum

From "Mathematics Rising" blog: 

"...mathematics is not built entirely on logic.  It lives somewhere between thought-governed ideal realities and physical realities created by the senses.  As such, it may be able to provide its own unique view of cognition itself.  It may be said that cognitive processes unfold themselves into mathematical insights."

Read the entire post on the essence of mathematics here:

http://mathrising.com/?p=335

Sunday, December 12, 2010

Friday, December 10, 2010

Weekend Miscellany

Just a little quickie recursive brain workout for starters:

1. The third sentence here is true.
2. This is the second sentence here.
3. The fourth sentence here is false.
4. The sixth sentence here is true.
5. The first sentence in this list is true.
6. The first and last word in this sentence is "the."

Is sentence #5 true or false???

Meanwhile, plenty of fun stuff at Sol's latest "Wild About Math" entry for the Equalis Community blog:

http://www.equalis.com/members/blog_view.asp?id=565749&post=116258

Thursday, December 9, 2010

"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.

Wednesday, December 8, 2010

"The World of Trotter Math"

I've recently been reading a lot of interesting posts, playing with numbers, over at "The World of Trotter Math," especially many recent ones on prime numbers:

http://trottermath.net/wordpress/

Upon researching to learn more about the site's proprietor I suddenly discovered his name was Terry Trotter and he passed away in 2004. I don't know who keeps the blog running, but thank you whoever is responsible.

A further-interesting tribute to Mr. Trotter is here:

http://www.guardiansofdarkness.com/GoD/trotter.html 

Sunday, December 5, 2010

Saturday, December 4, 2010

Gardner Strikes Again

For today's amusement, a paradox quoted directly from Martin Gardner's "The Jinn From Hyperspace":

"Now for a final paradox. There is a certain event that I guarantee will or will not take place during the next ten minutes. You are absolutely incapable of predicting correctly whether it will or won't occur. I don't mean that it's unlikely you can predict it. I mean it is logically impossible to predict it!
"You don't believe it? Then do the following. If you think the event will occur write "Yes" inside the blank rectangle below. If you think it won't happen, write "No" inside the rectangle.
"If you predicted correctly, I'll send you a million dollars.
The event is: You will write "No" inside the rectangle."


As Gardner might say, "Gotcha!"

This is just one of many paradoxes entangled with self-reference and classic problems of causation/prediction when dealing with human language and logic.

Thursday, December 2, 2010

Boys Will Be Boys...

...and also creative mathematicians:

nice storyline from "CTK Insights" on 3 young people who bucked the more mundane (and expected) answer on an IQ test to start with Pascal's Triangle and end up with "The Rascal Triangle":

http://tinyurl.com/29opquv

(a clear case of thinking-outside-the-triangle)

Wednesday, December 1, 2010

"Sexy Primes"

six is so sexy... "Trotter Math" introduces us here (in a re-post of info from over 10 years ago!) to "sexy primes":

http://trottermath.net/wordpress/sexy-primes/