11^6

Where were you 11/11/11 at 11:11:11? Here's me at the moment, in the minibus.

 

One of my former students in Washington used to always make a wish at 11:11. I just heard that this time, as she was making her wish, her boyfriend ran into the room with a ring saying his wish was to spend the rest of his life with her. Awesome! Congratulations L.Z.!

Mathematical Aesthetics in a Beautiful Town

One of my works from the 2011 Bridges Mathematical Art Conference in Coimbra Portugal made it into the Notice of the AMS. Here's a link to the article and a screen shot of one of the pages.

www.ams.org/notices/201205/rtx120500648p.pdf

xkcd puzzle

Here's a fun calculation from xkcd.com. Puzzle: why does this work? Can you find other numbers in which the same trick applies? Can you generalize?

Prime number chemistry

It's Forskningsdagene, or Research Days, in Norway. Many big cities have special events to celebrate science research. In Trondheim there are series of shows and lectures and the Research "Torg" (market/square/court?) Every year, the math center participates in the torg, and for the past few years I've been in charge of planning and coordinating the event with the university's math department.

The theme for this year was chemistry, so we decided to 'number chemistry'. I've always thought of the integers like molecules, with prime numbers as the atoms. We set up number molecule decorations, a prime number target game, and computers where visitors could find the prime factorizations of their phone numbers.

Students for the math department made the decorations and the ball toss game and did a very nice job. I wrote the program to find the factorizations, and we all made a variety of signs talking about primes, twin primes, the GIMPS project, and some prime number periodic tables that are pretty cool.

The game was a big success. Kids waiting in line were given a card with a number on it, maybe 18 or 54 or 770. The would need to figure out the prime factors by the time they got to the front. They would then throw balls at targets painted with primes, the goal being to knock down primes whose product matched the target number. Winners wrote their names on a sticky note and stuck it on the wall, enough of reward to make players proud without having to hand out candy.

Here's my periodic table of prime numbers, made to match the chemistry theme of the day and drive home the idea of "primes as atoms". Twin primes are colored gray, with symbols added for Mersenne primes, Sophie Germaine primes, Fermat primes, and palindrome primes. I think it came out nice!

I went through many iterations of the table. I harbored an unfounded hope that maybe by organizing the integers in a different form maybe some kind of cool pattern would pop out. Here's the periodic table shape with integers starting at 1 and all of the prime numbers colored blue. It turns out that even in the periodic table format, the primes appear to be patternless. I don't know whether to be happy or sad.

Math mistakes in kids' books 2

This symmetry error comes from "5 minutter historie" (="5 minute stories"). The concept of this book is brilliant, about 50 stories each that can be read in five minutes. In the story "Princessen som aldri smilte" ("The princess who never smiled"), a princess is cursed by her nanny to never smile unless someone can guess her (the nanny's) name. The king and queen hire professional name guesses and try all manners of amusing the princess to get her to smile, but nothing works. One day, a painter makes a funny picture of the nanny and writes AMME (Norwegian for 'nanny') on the painting. The princess catches sight of the word reflected in the mirror and guesses "Emma" as the nanny's name, and the spell is broken.

OK, so apart from the idea that the kingdom guess every imaginable name but somehow forgot to try the common name 'Emma', can you spot the errors both in the text and the illustration?

 

PS: upon discussing these errors with my 8-year old daughter, she had to try writing words and looking at them in a mirror to discover what word was written on the painting. Afterwards, she became so fascinated with backwards writing that she's been doing it for days, leaving me "secret messages" that can only be read with help of a mirror! Maybe mistakes can be awesome sometimes!

Math mistakes in kids' books 1

I found some math mistake in my daughter's bedtime stories this past month. The first comes from "Ask Mia", a storybook from the Math Matters series. This is an excellent story in which the characters are motivated to create a pictograph to convince a newspaper editor to change her idea of what the paper's content should be. On the final pages is a picture of the newspaper, including this puzzle:

Luis's Quiz: If a hen-and-a-half lays an egg-and-a-half in a day-and-a-half, how many eggs does one hen lay in one day?

The incorrect answer of 'one egg' is given. What is the correct answer?

Rock-scissors-paper-lizard-spock Puzzle

I got this T-shirt long before Big Bang Theory made the game popular. There's been something that's bothered me about the layout of the shirt, however.

The arrows are not symmetrical. They're pointing in haphazard directions. Here's the puzzle: switch just two of the icon circles (preserving the relationships) so that the arrows have rotational symmetry.

Human Geometry

Here's a video of some of my artwork. I created as a demo video for an exhibition application. The work is part of my Naked Geometry project. Thanks to my sister, Hez, for letting me use her music in this video. Enjoy!

Pendulum trick

Here's an animation I made with Flash. For every one trip back and forth that the top circle makes, the second circle makes 2 trips, the third 3 trips, and so on. Try with 2 or 3 objects to see better what's happening, then explore larger numbers (100-300 is nice).

Despite the simplicity of the math, there are lots of crazy patterns that pop up as you watch the strands weave and unweave. There are connections here to factors and primes. Notice how you can catch sight of, for example, 4 strands, then 3, then 5, then 2, then ...? What is happening? What is the pattern?

Decision Tree

This poem originally appeared in College Math Journal under the title "Tree Diagram". I was asked to reformat it for inclusion into a thematic literacy issue in the journal "Symmetry: Culture and Science". This is the new format: a tree!

There's a structure placed on the poem that creates an unusual result. The first line is the question, the second the decision, the third the reaction, and the fourth the future effect. There is then an angel-devil influence in the directions of the lines; movement to the left is leaning towards the 'good' and towards the right is leaning towards the 'bad'. What I found surprising is that many of the poem sequences in this tree are kind of depressing ("... now the chance has slipped away, I guess I'm doomed to live this way.") but there are two sequences that are special.

In the extreme left and the extreme right sides of the tree you can find two poems where you get the feeling the narrator feels good about his/her choices and is satisfied with the way life is going. While this may not make any flattering statements about morality, I think it does say something about consistency. In life, as in mathematics, we are free to choose which rules we will live by. Once you've done so, you should be consistent with these rules or you run the risk of being dissatisfied.

Can we really learn that from mathematics?

Artwork in Journal of Mathematics and the Arts

My artwork from the 2010 Bridges conference made its way into the Journal of Mathematics and the Arts (Volume 5, Issue 2, 2011). Here's a link to the article and a screenshot of the page with my artwork. The article has lots of examples of the good mathematical art that is celebrated at this conference.

The mathematical art exhibit at Bridges Pecs Hungary, July 2010

A visit with George Hart

I had the pleasure of visiting renowned polyhedra artist George Hart at his home in Stony Brook, NY this summer. His house is filled with his polyhedral creations -- no surface is left untouched by mathematical beauty in this geometry paradise.

We had a lovely afternoon playing with puzzles and talking math. George took us into his shop and demonstrated a very interesting cut on his scroll saw. By making a single spiral cut as he twisted a dowel down through a blade, he separated the wood into two parts, but not as I expected. The outer piece is hollow, and the inner piece is a wooden screw, like a corkscrew, that can twist in and out of the outer part. All made with one continuous cut. Amazing! Here's a link to a rather amazing explanation and an unbelievable example of four nested spirals made with this method: http://momath.org/home/math-monday-nested-helices/

 

George is an expert geometer, a supportive colleague, and a fascinating and all-around great guy. Check out more of his artwork at www.georgehart.com, and also check his MAJOR project, the Museum of Mathematics at www.momath.org.

Cube women sculpture

I made my first 3d printing models this summer. I thought it would be as easy as taking my 3d models I use for 2d digital art and converting the files, but in fact I had to rebuild from scratch, with special attention to hair and fingers and making everything perfectly symmetrical. The models then needed to be hollowed out and the walls given thickness. I was holding my breath when the package arrived from the printers – would they snap together as planned? Would they break? It came out perfectly. The figures snap together snugly, the fingers are strong and flexible enough to get a good grip, and the final statue sits flat.

Here's a few shots, with a coffee mug for scale. The sculpture is about 12 cm high.

You can order a sculpture of your own here if you like!

The Mike Naylor Trefoil

I had a curve named for me! A big shout out to Will Webber of Bellingham, WA who parameterized one of my favorite shapes to doodle. I used to draw this freehand in my classes, and enjoyed exploring variations with number of loops and number of whorls. None of my sketches ever looked as good as Will's calculated version shown here. Thanks Will!

(Will is a master with parameterizing, you should see him in action as he waves his hands back and forth, gets a feel for the separate x- and y- motions, and then nails the equation. Inspiring!)

My favorite palindrome

 This took a while to learn to say, but I like to pull this out when palindromes come up in conversation:

A man walks into a bar and says, "Syas dna rab a otni sklaw nam a!"