Vision Under the Influence of Math

Here is a pic from the Flickr photo group called "Everything's Geometery". It is a continuous stream of people posting photos that reflect a geometric/mathematical aesthetic. I'm not sure what that means. Maybe clean lines. Traditional figures. Order. I'll ask Carianne later. I do know that the photos tend to be similar to the types of visuals that arrest me as I go through a day. One of the most common photos types in this stream involves stairs, particularly the play of shadow on stairs. I'm not sure why that is so powerful, but if you have ever stopped to admire a staircase climb the side of a building, you might be a math geek.

pic by Juilien'

Shirley Ellis's Name Game

Probably one of the coolest algorithms of all times. I love the fact that the name game is not a song, but a means to generate a whole series of songs given a cede. Formally, the name game is a lot more interesting (if not a little sillier) than a normal song. The Name Game is the brain child of Shirley Ellis. She recorded it in 1965. (Somehow I thought the song was much older.) The placard below is from some promotional material of the time, and actually explains the rules (or algorithm). Note the exceptions so we don't end up swearing.

Geek of the Week: Lee Bradley

Welcoming the newest member to our math community Lee Bradely. Lee has just been hired on as a full time math tutor in the Academic Support Center. He gave me a great problem. You have to create 5 rectangles, such that the length of each side of one of the rectangles is an integer 1-10. You have to use all 10 numbers, so no sides of the same length. Furthermore, the resulting rectangles have to tile together to form a square. He has sworn there are 4 solutions and has given me one. Stop over in the ACS to say hello and get a hint from him. Also check out Lee's website. He uses mathematics to make beautiful puzzles.

Numbers Everywhere

This has to be a familiar phenomenon for anyone who spends a good part of each day working with numbers. I'll often look at the clock and get a charge out of the fact that it is 12:34, or 12:21, or 3:57. Just as geeky, getting excited about a friend that lives on 169 W Center St. (I mean imagine if your address was a perfect square!) There is a famous anecdote of the mathematician Ramanujan (the self-taught prodigy mentioned in Good Will Hunting). He was visited by GH Hardy who rode in a taxi with the number 1729. Hardy asserted that it was a dull number. Ramanujan still laying in bed said, it was the smallest number expressible as the sum of two distinct pairs of perfect cubes (1729= 1^3+12^3=9^3+10^3). This is incredible to come up with off the top of the head. My geek powers extend nowhere near this far. But....I did I pick up my father in Boston last weekend and loved the fact his conference hotel room was 735. 7 divides 35, cool. And 7,3,5 are the first three odd primes. Just had to share. Enjoy the pick.

Literature Numbers

Fenimore Cooper used almost eleven hundred Shakespeare quotations as epigraphs and/or chapter headings in his thirty-plus novels.

From The Last Novel (David Markson)

Geek of the Week: Jesse Abbot

Jesse pulled off another great evening in his Proof & Possibility series. Barry Loewer was incredibly engaging as he walked us through the potential philisophic implications of quantum physics. I know nothing about physics and was riveted. When's the next one? (btw, it was packed make sure to get there early next time if you want a good seat.)

If you missed it, they should have a podcast of the lecture and Q&A pretty soon.

(Sorry about the pic Jesse. I have to get a better camera. I'm still at 4 Megapixels. That is nowhere near geeky enough.)

Really Cool Visual Algorithm for Multiplication

One of my students in math for Liberal Arts dug this up on YouTube. I had never seen this technique for multiplication before. I love it--completely visual. Thanks, Rachael!

Pi, Pi, mathematical Pi...

This post is for our resident classic rock junkie, Rob C. (Sue and I caught him singing Simple Kind of Man in his office last night.) Stay tuned maybe we can get him to play this for the pi contest this year.

Pi Song

Thanks for the link, Jay!
Pic from revlimit

Argazzi's New Puzzler

Paul sent me another fun problem. It is a complete the sequence problem.

Next term in this sequence is?
1
11
21
1211
111221
312211
13112221
1113213211
...

Any one got it. This one's driving me nuts.

New Math

New Math was an educational movement in the 50's/early 60's (?) to increase the rigor of mathematics education in grade schools. Among other things it stressed doing arithmetic in different bases. This of course caused a great deal of consternation among parents as they brought home there homework and told there parents with great conviction that 3+2=11 (and of course they were right in base 4). Lehrer's song parodies parental exasperation.



It is widely assumed that we have a base 10 system because we have 10 fingers, our hands being the original calculators. I read in Number (Dantzig) that many have advocated giving up are base 10 system for base 12. The reason being there are twice as many base divisors (2,3,4,6) than 10 (2,5). Divisibility is extremely easy to test for base divisors. Think about how easy it is to tell whether a number is divisible by 2 or 5. In fact most of our temporal and customary measures are base twelve. There is also a competing logic. The great mathematician Lagrange argued for a prime base like 7. Can you guess why?

The Logic Below

I came across this in the 27th Canto of the Inferno. A few lines grabbed my attention in the confession of this condemned spirit.

I was a man of arms, then Cordelier,
Believing thus begirt to make amends;
And truly my belief had been fulfilled

But for the High Priest, whom may ill betide,
Who put me back into my former sins;
And how and wherefore I will have thee hear.

While I was still the form of bone and pulp
My mother gave to me, the deeds I did
Were not those of a lion, but a fox.

The machinations and the covert ways
I knew them all, and practised so their craft,
That to the ends of earth the sound went forth.

When now unto that portion of mine age
I saw myself arrived, when each one ought
To lower the sails, and coil away the ropes,

That which before had pleased me then displeased me;
And penitent and confessing I surrendered,
Ah woe is me! and it would have bestead me;

The Leader of the modern Pharisees
Having a war near unto Lateran,
And not with Saracens nor with the Jews,

For each one of his enemies was Christian,
And none of them had been to conquer Acre,
Nor merchandising in the Sultan's land,

Nor the high office, nor the sacred orders,
In him regarded, nor in me that cord
Which used to make those girt with it more meagre;

But even as Constantine sought out Sylvester
To cure his leprosy, within Soracte,
So this one sought me out as an adept

To cure him of the fever of his pride.
Counsel he asked of me, and I was silent,
Because his words appeared inebriate.

And then he said: 'Be not thy heart afraid;
Henceforth I thee absolve; and thou instruct me
How to raze Palestrina to the ground.

Heaven have I power to lock and to unlock,
As thou dost know; therefore the keys are two,
The which my predecessor held not dear.'

Then urged me on his weighty arguments
There, where my silence was the worst advice;
And said I: 'Father, since thou washest me

Of that sin into which I now must fall,
The promise long with the fulfilment short
Will make thee triumph in thy lofty seat.'

Francis came afterward, when I was dead,
For me; but one of the black Cherubim
Said to him: 'Take him not; do me no wrong;

He must come down among my servitors,
Because he gave the fraudulent advice
From which time forth I have been at his hair;

For who repents not cannot be absolved,
Nor can one both repent and will at once,
Because of the contradiction which consents not.'

O miserable me! how I did shudder
When he seized on me, saying: 'Peradventure
Thou didst not think that I was a logician!'


Never has violating the law of the excluded middle had such dire consequences. One might be interested that logics have been posited that deny this law. Play these logics at your own risk. The black angels are watching.

KenKen

Christina sent me a link about a cool new puzzle called KenKen. It is Sudoku-like, but involves arithmetic as well. Here is board. This is my understanding of the rules. A four by four board can be covered in the numbers 1 through 4 with no more than 1 of each being each row or column (like Sudoku). However, the board is divided into subregions or rectangular boxes. Take the first two boxes in row 1. That is a subregion. The two and division sign say that only the two numbers that occupy the box have to have a quotient of two. So you could fill in 4,2 or 2,1 for the first two boxes. Interesting, huh. And for teachers this could be a fun puzzle to work with classes. (In fact it was invented by a Japanese teacher.) The Times even has a lesson plan for you, or play just for fun online. Thanks Christina!

Math-Toon

Laura G. tipped me off on Sunday's Foxtrot's Fibinacho action.

Flight of the Conchords

I'm a sucker for any math visualizations of personal lives. Sue told me about a show she watches: Flight of the Conchords. I'll spare you the weak premise, but there are two musicians and a manager. The manager in last night's episode decides that their relationship should go from being strictly professional to friends. The funny part of this is the completely business-like manner in which the manager tries to accomplish this transition. Why am I interested? He uses a graph to explain. His theory is that the closeness of relationship is proportional to the amount of time one spends together. (That would of course make your coworkers your best friends, but don't get hung up on the details.) Here is a Youtube clip of the description. (You'll have to fast forward to about 1:53.)



Later in the show, the musicians have failed miserably at being friends. Here is the manager's graphic summary of the duo's blunders. (Fast forward to the 6:00 min mark.)



Thanks, Sue!

Venn's for Sue

Sue's class is doing Venn Diagrams, so I thought I'd include a two more of my favorites. There are a ton of funny/cute uses of Venn Diagrams. It is definitely the one part of math that has stuck for every graphic designer.

Explain your next breakup with a Venn Diagram. Fuffer on Flickr


I call this the intersection of snarkiness.(You'll probably have to blow this one up to see it.)


This is pure wise-assery. Kevan on Flickr


Also, check out my personal favorite in this previous post.

You Venn Again

Look what I found in Rolling Stone. Party like a math-star.

Twitter's Rising Popularity < Twitter's Rising Cost ?

I picked this up on a data mining feed. A really interesting discussion is brewing on how much it costs twitter to maintain it's network. The worry is that users getting SMS messages are going to eat the network out of house and home as the network gets larger. Here is a really simple demonstration of where the worries come from. Say it costs twitter $100 a year to maintain a the correspondence between any two users.



One can see adding a third user increases the overall cost of the network by $200. Adding the fourth will increase the cost by $300. You see where this is going. The fifth member will increase the cost by $400...and the nth member will increase the cost by (n-1)*100.

Now Twitter's actual case is much more complicated. First, each new member doesn't connect with every single old member. Second, some links cost more than others. Third, the more members, the greater twitter's add revenue (I assume they are add-based). This helps offset the greater costs.

Curious? Here is Paul Botin's post that started the discussion.

I came a cross the discussion reading Mathew Hurst's critique of Botin describing the growth of costs as "exponential". The math snark in me also laments the imprecision with which this word is often used.

Figuring Out the X Hex

For all you math educators, Christina sent this on to me. You might be interested sitting in on this seminar.

Free Live Webinar:
Why Students Struggle with Algebra and How Schools Are Helping
When: Tuesday, February 10th at 1pm Eastern time.
Free registration is now open at: http://edweek.org/go/algebra
One of the biggest challenges in K-12 education today is how to help students overcome their struggles in introductory algebra. Many students fail or are barely able to keep up in their first algebra course, typically taught in 8th or 9th grade. In response, state and school district officials are trying to solve this problem in several ways, such as by encouraging better teacher preparation, including an emphasis on algebra, and by revamping courses and curricula to help struggling students, such as through the creation of "algebra readiness" classes aimed at girding students for the challenges of that class. In addition, policymakers at all levels have called for an improved, more streamlined approach to teaching elementary and middle-grades math as a way of preparing students for algebra.
This webinar will bring together a number of experts who have examined students' experiences with algebra. One of the goals is to explore the fundamental question: Why do so many students find algebra so difficult? The webinar will then examine efforts by districts and private curriculum-developers to help these students. It will also touch on major developments at the national level in this area, such as the release last year of a report of the National Math Advisory Panel, which called for more coherent math curricula at early grades as a foundation for algebra.
About the Guests:
Jon R. Star, Educational psychologist and assistant professor of education Harvard University.
Mary Jo Tavormina, Elementary Mathematics Manager, Chicago Public Schools.
Jesch Reyes, Math specialist, former algebra teacher, Chicago Public Schools.

My Head is Spinning

A number of two digits is seven fourths of the number formed by interchanging its digits. If the tens digit is two more than the units digit, what is the number?

Steve Luko sent this one in. Thanks, Steve!

pic by beth.mckenna