Multiplication is NOT repeated addition (multiplication as 'scaling', from Keith Devlin):
http://www.maa.org/devlin/devlin_01_11.html
Friday, December 31, 2010
Tuesday, December 28, 2010
Logic...
Nice quick introduction to several classic paradoxes here:
http://www.popgive.com/2010/06/brain-twisting-paradoxes.html
http://www.popgive.com/2010/06/brain-twisting-paradoxes.html
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
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.
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.
Sunday, December 26, 2010
Saturday, December 25, 2010
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/
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/
Monday, December 20, 2010
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
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/
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
http://tinyurl.com/22juwgm
growth in interest in arithmetic, not so much:
http://tinyurl.com/25km6aq
Thursday, December 16, 2010
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! ;-)
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
"...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
Google Hidden Challenge
Interesting geeky story of Google planting Mensa-like problem in an ad and rewarding solver:
http://tinyurl.com/27v3mgq
http://tinyurl.com/27v3mgq
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
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.
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
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
Mathematicians, Media, and Sex Appeal
Entertaining post (including lots of links) today from Jonathan Farley of The Guardian:
http://tinyurl.com/27qmk42
http://tinyurl.com/27qmk42
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.
"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)
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/
http://trottermath.net/wordpress/sexy-primes/
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