Part 1: http://youtu.be/ahXIMUkSXX0

Stay tuned for part 3, where we solve ALL the mysteries. Well, sort of. Coming soon! (2 weeks?)

We'll be doing a Q+A! Submit questions for us at this link: http://dft.ba/-vikhan, and keep an eye on the khanacademy channel because we're gonna upload an answer video in a week!

The official announcement video: http://youtu.be/eWuAYoHysIo

Sal's you tube channel: youtube.com/khanacademy

www.khanacademy.org

How will this affect my work? Well, previously I lived off of speaking fees, ad money, and donations. Now I get to spend less time in airports and more time making videos, plus videos are now ad-free! I also have more resources and am surrounded by awesome people doing awesome things, so basically this is good for everyone.

Low-Frequency Blues

Origami Proof of the Pythagorean Theorem

Doodling in Math Class: Squiggle Inception

Also, did you know I have a twitter account that rarely gets used? I'm @vihartvihart

Also MoMath has this cool presentation series. You should go to the next one, because I'll be introducing the supercool speaker, Scott Kim.

With 45 more swords, this pattern could be extended into a full icosadodecahedron-type shape, where the sword blades make the triangles and the handles make the pentagons. With rigid swords, the shape would even hold itself together with no wire or glue. As it is, it makes a very nice hat:

And then it was time to go. I had a wonderful time, met many wonderful people, and had a big wonderful space to play in. Here's what it looked like as of yesterday morning:

I want to emphasize the improvisatory and collaborative nature of the week. Most of the time, I had some sort of vague plan/inspiration, and it was really through the help and input of other people that things ended up being awesome.

I'd say "Hey, I got these things. Let's try connecting them like this and see what happens. Then maybe we can hang it somewhere or something." We'd try it out, see what potential problems were, and do some bugfixing. The result was an amazing week and a big room full of fun stuff.

I'm interested in finding a longer residency of this sort. And looking forward to hopefully returning to Pfoho next year!

It's made of 32 baskets arranged like the faces of a truncated icosahedron (that's the shape of a soccer ball). The 20 "hexagons" are in shades of blue and green in a 5-color pattern. The 12 red baskets are like the black pentagons on a standard soccer ball. It's a little imposing to sit under. Here's how the dining hall looks, as of last night:

There were clothes hangers, dolls, clipboards, and protractors.

Here's some vertically-oriented photos.

There were also sponges, plastic containers, crayons, and wooden spoons.

The people at the crayon table were extra diligent, staying longer to figure out how to make a crayon-tip polyhedron and how to use the wrappers to fold intersecting tetrahedra.

Inspired by the three-fold symmetry clothes-hanger arrangement someone had made, I later grabbed some help and made this:

Then it was umbrella time! I made the residents start unpacking the umbrellas, and went to get some materials. I know that my mathemusician-in-residenceship has had some effect, because when I got back, this is what greeted me:

Awesome. Then we got started on connecting the umbrellas into a hyperbolic plane. Between us all, we figured out a good way to build and display it. Then something magical happened. Some students had the idea of writing poetry on the umbrellas, so we got out some white-board markers and turned the hyperbolic umbrella surface into a big collaborative writing/drawing space.

I love collaborative sculpture! I'm thrilled with the result. It would have never happened without the creative input of many people.

I decided they should be a giant dodecahedron. I guess I'm at that point in my Mathemusician-In-Residenceship that I can gesture vaguely and people will know what I'm talking about, because after explaining just a little, I was able to sit back and drink juice while everyone else did the work (I didn't even have to take the photos! These are by the lovely Janice He).

The dining hall is beginning to shape up rather nicely.

The Harvard Crimson also put out this nice video covering the events from the balloon workshop the night before:

Various groups of people wandered in and out of the dining hall throughout the evening, and we made a bunch of different things, including some snub pfolyhedra in Pfoho colours.

It came together nicely! Thank you to everyone who helped, whether it was by constructing, hanging, or cheering us on.

There's also a photo of me demonstrating some balloon techniques on the front page of the Harvard Crimson. I also just bought a ton of supplies for the workshop I'm giving on Friday, which should be pretty crazy, so don't forget to come by if you're around.

For some residents, being trapped wasn't all bad.

If you take your paper cross (which you can cut from a square in a single straight cut, if you fold it in half three times) and put a mobius twist in each of the loops, the result is quite different! I first heard of this trick from Mike Caputo (who has an article about it in the Jan/Feb 1990 issue of TOMT), and there's a nice YouTube video by Daniel Keogh demonstrating the process.

Soon we moved on to exploring new shapes to cut in half. I especially like this variation, by Anne Goetz: start with an eight pointed asterisk, and connect opposite ends with a twist (be sure to twist them all the same way). The result was very surprising to me. We explored more, and it seems to generalize to all Mobius asterisks with 6 or more points. I'll let you try it for yourself, rather than ruining the surprise.

Another student, Carlos Rodriguez-Russo, found a variation that when cut in half yields a trefoil knot. And if that's not enough to keep you entertained all night, here's one last puzzle. What asterisk shape, twisted how, gives the result below when cut in half?

I'm quite excited by all the cool cut-in-half things we discovered last night. It's going to be a fun week.

Click to play (3 min 38 sec)

And then that reminded me of an entirely different piece of music, a song I wrote and recorded last year but never posted as it's a bit different from what I usually throw up here. Today is a day for different things, so here it is.

Click to play (3 min 48 sec)

And here's a short video I made with my bro last night.

1.

Some sort of thing

Click to play (2 min 20 sec)

The problem with it is that it's not really its own thing; it's got a melody partly stolen from the middle of another little piece of mine, and a lot of the chords are also from a different piece I've been working on. But different elements of different things tend to jumble together in my head and get stuck together, so there it is.

And it's collapsible!

Also, check out the science section of the New York Times tomorrow (Jan. 18)! Kenneth Chang wrote this awesome article about me.

See the Wikipedia page on linkages. For more in-depth information about the mathematics of linkages, go to 16:05 in this lecture.

I've been wanting to make this particular tiling for a while now, and as far as I know this is the first physical version of this tiling ever made out of any medium. Each vertex is surrounded by exactly three triangles, one square, and one pentagon. Needless to say, I was delighted with the result.

After the workshop, I added one last piece with Glen Whitney, MoMath executive director, and together we hoisted it up onto the top of the MoMath booth where it lived for the remaining duration of the conference:

You can find just the song here: http://vihart.com/music/gauss12days.mp3

It was pretty awesome.

This one is done YouTube-style, but I'll get the non-YouTube one up along with a page in the candy section of the mathematical food page sometime in the future.

You can also now 'like' my new facebook page, if you like.

This 3d printer is a robot that spits out plastic layer by layer. In the first photo it's about 3/4 of the way up. The second photo shows the finished piece. I think it's super awesome to be able to think of, design, and then print out a 3-dimensional mathematical sculpture during the course of dessert!

If you've got an iPhone/Pad/Pod, you can check it out, hear my music, explore, build, blow stuff up. I like that the world-generating algorithm makes nice spacious caves. There's plenty of potential for mathematical building, too-- if you make something cool (Menger sponge and other cellular automata come to mind), please send me a screenshot!

The three videos are now on this webpage, which maybe someday I'll update with some more explanation and info, but for now just has helpful Wikipedia links.

"What does it look like when you crease the hyperbolic plane? This painting is an attempt at visualizing simple origami done with hyperbolic paper. Each plane has a mountain and valley fold perpendicular to each other. Done with your average Euclidean sheet of paper, it would be impossible to have both creases folded at a non-zero angle, but the hyperbolic plane can fold both ways at once. The creased plane can then be manipulated into different 'birds', or so I imagine."

I will also be speaking at JMM, giving a talk of the same title. You can find me somewhere in the vast program. If you're attending JMM, be sure to come say hi!

Thank you to all the people I know whose math classes do not require such pastimes!

I made a sketch for this last night. Today when I came back to it, there was a dead fly on the web. Spooky!

Each platonic solid is made using smarties, hot glue, and patience. I used some of the extras to make this scary scary skeleton:

1.

Give Me Your Anger

Click to play (3 min 28 sec)

It's not a genre that I've posted before on this site, but I find a large part of my creativity comes from working with a large variety of subjects, mediums, and styles.

I built this starting from the top with one piece, and following the simple rule that for each layer, put a new piece below the spots where there is exactly one candy corn bottom corner. The process is explained with diagrams in a new page on candy corn.

There are 60 lollipops arranged with icosahedral symmetry, five each of 12 flavours. The first photo shows the whole ball, looking down at one of the 3-fold axes. The bulkiness of the wrappers makes it difficult to see the structure from the outside, but an inside view centered on one of the 5-fold axes reveals that the sticks are carefully arranged.

Each of the twelve pentagons has one of the twelve flavours circling it. I still have a bunch of extra lollipops, so there may be some more lollipolyhedra in the future... but there's so much other Halloween candy to mathematically explore as well!

They've been appended to the end of the fruit polyhedra page in the Mathematical Food Index.

Not only will it never threaten to stab you, but two of the vertices squeak, and it is "durable for hours of play!"

I started by making the dihedral group of order 6, D₃. Just building the graph is not enough—I then used a sharpie to draw the direction of each edge. I might do more of this in the future, but I have to learn more first!

The new page has some new photos and results of a couple fruit-drying experiments, such as slicing the apply from top to bottom, or removing the skin before drying. There is still much work to be done in this delicious field of research; let me know if you have any ideas!

The large roundity of melonness made this easier than carving the apple, and I'd also had more practice! The lack of core also made it easy to carve out the faces to achieve Leonardo-style edible polyhedreality. For now I snuck these photos in at the bottom of the fruit polyhedra page, but I'm considering doing more advanced melon-carving in the future... I also know what I'm doing with my pumpkins this Halloween.

I wanted a light and airy hyperbolic plane that would float in the breeze. I decided to try making one out of plastic bags. I cut them into heptagons, ironed them together, and voila! The ironing was not easy, but it worked. I took some pictures of the process and plan on putting together a webpage soon.

To simulate the ghost drawing in a photo, I dressed all in black, wrapped the hyperbolic plane around my waist, and belted it into place. All I need now are proper lighting, camera, and a wind tunnel!

After my first two hyperbolic figure studies, I wanted to imagine more complex forms, forms that loop and fold in a sort of hyperbolic origami. In doing this, I accidentally re-discovered surfaces like Schwarz's P surface, which as it turns out can be made by rolling up a hyperbolic plane. While both those things are already known, I'm still going to give major points to mathematical art because they just as easily might not have been. Hopefully after a few more series of sketches I'll be entering new mathematical territory.

I'm sure there's others of you out there who have, or at least understand, the compulsion to make all five platonic solids once you've made just one. They're currently sitting in the fridge, waiting for the sun to come back out so that I can cut them up some more and take more photos, and then put together a savvy webpage.

In other news, scientific testing of the hyperbolic properties of dried apple slices is progressing. More on that soon.

This observation brings up two very important questions. Firstly, why do apple slices do this? There's some transformation that is turning a flat Euclidean slice into a hyperbolic one. One would think that in the drying process all cells would get uniformly smaller, which would make the whole slice simply shrink into a smaller flat slice. I'm currently conducting some more research to try to gain insights into this process, which will soon turn into a webpage.

Secondly, why is there nothing on the whole googlable internet about this? Is it really that no one has noted this before, despite that we see hyperbolicness every day in dried food such as potato chips? I can begin to answer this by asking why I myself never noticed this before, and by asking why people have in fact noticed the negative curvature of Pringles, which are relatively hyperbolic.

I think the answer lies in that people are not used to the many forms the hyperbolic plane can curl into, when embedded in Euclidean space. I myself didn't see these "wild" hyperbolic planes as what they were until I started playing with, visualizing, and drawing hyperbolic planes in different configurations, and even then it took someone else pointing it out to me, based on one of those unconstrained drawings. People saw it in the Pringle because the Pringle takes a more standard and recognisable saddle-shape, yet missed the connection that Pringles are an idealized version of potato chips, which have similar geometry. This speaks of the value of mathematical art, and collaboration between fields and people.

Click to play (1 min 32 sec)

When writing this music, I tried to capture the repetitive rotational feel in the process of both glassblowing and this particular instance of paper folding, as well as sneaking in elements of symmetry and mathematics. I see this video as a collaboration and communication between art, glass, music, math, paper, and people.

I think the colour makes it much easier to see what's going on, though seeing is really no substitute for playing with it in your own hands, so I recommend you make your own.

One neat thing about this is that by drawing freehand I have no limitations except for my own ability to visualize hyperbolicness; it tests my visualization skills and allows for forms that might not be found by other methods. I hope to take the concept further once I develop my drawing skills and hyperbolic intuition a bit more.

The first photo shows the three platonic solids that have triangular faces, and the second photo is of a hyperbolic tiling that has seven triangles around every vertex. I plan eventually to put a webpage together with more details and instructions. Mostly I'm glad that I had a stockpile of empty bottles lying around!

I put up a new webpage on hyperbolic beading so that you can make your own. So far the page only contains diagrams for the above model, but I hope in the future to try some other tilings and patterns.

I consider this a rough test for future mathematical beadwork, hopefully with nicer beads, colour patterns, and artistry. I was inspired to pursue mathematical beadwork by some of the very beautiful models I saw at BRIDGES this year, notably the works by Laura Shea and Bih-Yaw Jin. There are also some connections between computational balloon twisting and computational beadwork (if you wanted to minimize the length of the path the string takes).

I also put up a small page on Sierpinski's Tetrahedron. I'll be leading a workshop where we make a large one at the BRIDGES conference in two weeks. But first, I'm off to Paris to speak at the ESMA conference!

To get a sense of the kind of wonderful things he's inspired, check out reports from this year's Gathering for Gardner, such as this article by Bob Crease in The Wall Street Journal, or more recently, this one by Alex Bellos in The New Scientist. The building of the balloon snub dodecahedron mentioned in that article is shown at right, and the print version of contains a rather large picture of myself holding a balloon octahedron in front of my face.

You can read the full article, in Greek. Here is my interview, in English:

SK: Judging from the content of your site,you seem to love both noise and melody equally? Why do you think these extremes inspire you?

VH: The difference between music and noise is all in how you listen. So much music has become noise, background in restaurants and stores. It makes me worry we've forgotten how to really listen. But when we do listen, even noise is fascinating. There is so much sound around you at this very moment—notice it!

SK: What was the initial idea to set the paper instruments on fire?

VH: It seemed obvious. Flaming instruments have been done before, but to me it is heartbreaking to burn something as beautiful and difficult to make as a piano. The idea fascinated me, but I couldn't do it. But the paper instruments, while I'd spent many hours crafting some of them, are easier to destroy. Maybe because I created them in the first place.

SK: I 've seen some experimental musicians to set fire to their pianos but the nature of a burning paperwind(?) is much more impressive since breath and air consequently are so crucial for both fire and sound to exist.What do you think?

VH: Yes, that was one of the most beautiful things about it! Our breath was translated into not only sound, but also light. I think we all felt like dragons. So many people have made visual representation of music, but this was more than a representation—the fire was dancing with us.

SK: How was the experience during the playing? (emotions,the alteration of the sound during burning,injuries maybe)?

VH: We were improvising, and improvising is a wonderful thing. When you improvise, you are discovering together. One person discovers a rhythm, the next discovers a melody that fits the rhythm, and so on. But with fire, we were also discovering new ways to use our instruments, ways to manipulate the flame, and ways to play with light. This was a part of improvisation I had never experienced before. We had to adapt to the changes we each made in the music, and to what the flame did to the instruments. Fire is a great metaphor. We shared the flame, passed it to each other, supported each other's inner fire.

SK: In the relevant text of the video you are writing about the music's dependency on the ephemeral.Could you develop your thoughts on this statement?

VH: There are such beautiful moments in music, that climax which you wait for through the entire piece. But you can't take a snapshot of that moment and hang it on a wall to admire at your leisure. As soon as you try to isolate it, it becomes meaningless. You need the music leading up to it, and you can only stay there for so long before you have to move on. Even in dance, another art form strongly embedded in time, we can enjoy a still image. Music cannot be caught—it is there one moment, and then it is gone.

SK: "You are the last person who will ever play that burning instrument." This is definitely one of the strongest lyrics I've ever heard even though it's not supposed to be one. What do you think about the human condition are we just one-use burning instruments in a way?

VH: I'm not sure which is more ephemeral: music or humans. If we are just one-use burning instruments, who is playing us? I am quite certain that, more than I play music, music plays me. I'm sure many other composers feel the same.

Click to play (3 min 36 sec)

Also available on YouTube.

1.

Doodle in A Minor

Click to play (5 min 15 sec)

And I finally am posting recordings of a couple piano doodles in C Major from 2005–2006.

2.	Doodle in C #1	Click to play (5 min 5 sec)
3.	Doodle in C #2	Click to play (10 min 57 sec)

I also updated the recording of Nothing Has Changed quite a while ago, but in case you missed it, here it is:

4.

Nothing Has Changed

Click to play (5 min 19 sec)

The trouble with being a composer is that I always hope some day I will be able to play these pieces perfectly, so that you can hear exactly what I was trying to get at, but that day never comes and I eventually get bored of the piece and stop playing it altogether, which only makes things worse. But I would rather get out an imperfect recording than none at all, and I will trust you to forgive my mistakes.

Click to play (1 min 42 sec)

Also on YouTube.

Click to play (2 min 53 sec)

Also available on YouTube.

I've also added a webpage for Music Boxes. There's nothing new there yet, but there will be soon!

In other news, Storia is now in the iTunes music store. It's been updating every week, with three episodes so far. The RSS is separate from my blog, so make sure you're subscribed! You have lots of options: RSS, iTunes, or Google Reader.

I'm incredibly excited about this project because it is so much fun to be writing stories and music for each other. I've been writing stories and music separately for years, and putting them together has turned out to be really effective! I've already recorded a few episodes and can't wait to get them out.

So head on over to the Storia webpage to hear the tale of a mysterious ghost ship...

Yes, one of the many fun people I hung out with was Mike Naylor, the mastermind behind Naked Geometry. A group of us got together and tried doing some human geometry. Here is a cube we made with ourselves, and a lovely tessellation that Mike created out of me.

Click to play (1 min 51 sec)

Also available on YouTube.

For comparison, you can listen to the theme in piano from the Harry Potter Septet. This section is inspired by Dumbledore's speech at the end of Book 4, and spans from the theme entrance to the end of the movement.

Click to play (3 min 21 sec)

Mostly I am posting to provide a high-resolution version of the comic, as Blizzard requires submissions to be small jpgs.

You can see my comic on the official site. If you are not in the US, change the region setting in the upper-right corner, and select June.

I also spent the day making magic balloon octahedra for people. Here are some pictures from the event:

A girl sets the dials on the organ function grinder, while her friend inserts a number ticket.	Making a balloon octahedron wand (orange), watched by a girl who just received one (light blue). In the background, people ride square-wheeled tricycles.

Learn more about the other exhibits at the Math Midway on their website.

Click to play (1 min 43 sec)

Also available on YouTube.

I will be twisting balloon octahedra for children of all ages at the Math Midway premier next Sunday (June 14th)! There is a small green one in the photo, but I can make you any color you like.

The 12,000 pieces are for an "organ fuction grinder." You choose a number to input, and set some dials to various mathematical transformations. Not only does the number get put through the transformations, but a musical theme also! For example, if you add three to your number, the melody gets transposed up three steps. It's very cool to play with the Mathematica version, programmed by George Hart, and I plan to get an online version up in the future.

The rest of the Math Midway exhibit promises to be really fun too. There will be a tricycle with square wheels which, as you can try for yourself, gives a perfectly smooth ride! There will also be giant puzzles and other cool stuff.

Click to play (4 min)

Also available on YouTube.

A bunch more paper-instrument stuff is coming soon, so stay tuned!

1.	Storm	Click to play (1 min 55 sec)	Also available on YouTube.
2.	Didgeriduel	Click to play (1 min 37 sec)	Also available on YouTube.

Before we burned all the instruments, I made some studio recordings. Here are three short pieces for paperwinds and paper tube xylophone:

1.	Dance	Click to play (56 sec)
2.	A3 A4	Click to play (1 min 32 sec)
3.	Floo-ee-oo-ee-ute	Click to play (1 min 38 sec)

Related to this paper is a seven-movement piece in which each movement is inspired by and contains the symmetry of each of the seven frieze patterns. The piece will ultimately be a piano trio, but three movements of the piano sketch are now available:

1.	Dizzy Hop	Click to play (1 min 28 sec)
2.	Hop	Click to play (1 min 26 sec)
3.	Sidle	Click to play (2 min 18 sec)

1.

Altitude Beta Theme

Click to play (2 min 9 sec)

A commission like this is a collaboration between the game designer and composer, and we have to work together to get the feel of the music to be just what the game designer envisions. The first draft of the music contained three different ideas I was playing around with. We ended up going with something more serious, but you might enjoy listening to the original:

2.

Altitude Theme Draft

Click to play (3 min 9 sec)

1.	Storm	Click to play (1 min 43 sec)
		A piece for paper xylophone and assorted paper winds.
2.	Didgeriduel	Click to play (1 min 16 sec)
		A piece for two dueling paper didgeridoos, paper tube harp, paper drum, and--unintentionally--dog.

Here's a picture of the band rehearsing. From left to right: Frank Maes on paper drum, a blurry Hendrik Goris playing the paper xylophone faster than the eye can see, myself adjusting a paper slide-flute (note that the skirt is made of paper as well), and Stefan Langerman on the paper hand-flute. In the corner you can see the two black tubes of the tube bass, and most of the giant didgeritube.

So you can get an idea of the theatrics behind the didgeriduel, here is Stefan with the giant didgeridoo which extended into the audience (it is not at full length in this picture), and myself with a comparatively small didge.

Here is Hendrik playing the tube harp. Like the paper xylophone, the pitches can be adjusted easily by changing the lengths of the tubes.

1.	Dizzy Hop	Click to play (1 min 28 sec)
2.	Hop	Click to play (1 min 26 sec)

1.

Nothing Has Changed

Click to play (5 min 19 sec)

Vi Hart, a Stony Brook University senior music major, has been wild about Harry since she was about the same age as the adolescent wizard in J.K. Rowling's first novel, “Harry Potter and the Sorcerer's Stone.” Hart will conduct the premiere of the “Harry Potter Septet” she composed for string quartet, violin, piano and two female voices. It's based on all seven Rowling books in the series.

The book that launched a thousand marketing schemes has now spawned a classical chamber piece, composed by a Stony Brook music major with a flair for mathematical wizardry. The Harry Potter Septet [is] an ambitious but accessible composition for string quartet, piano, and two female voices... It's the work of multi-talented senior Vi Hart, whose obsession with J.K. Rowling's adolescent sorcerer dates back to the sixth grade.

“I'm a composer and I've been composing for as long as I can remember. I got inspired last year by none other than the Harry Potter series. The project started off as a cute idea and then I just ran with it. It took about 14 months. But I completed a septet—originally 2 hours of music, which I've cut down to one and one-half hours.”

“I think there's definitely a connection [between music and mathematics]. Maybe I'm biased because those are the two things I know how to do, so they're the only things I know how to see connections between. They're similar in that sense of discovery, having things fit together. When I'm composing a piece, I often feel that I know what has to come next and what makes sense. Certain notes work and other notes don't work. If you can figure it all out and put it together, you end up with a beautiful piece. Mathematics is often the same way where you're on this trip of discovery. Certain things work, certain things don't. And when you're done, you have something beautiful, elegant.”