Over seven months after building my first Hexastix, a geometrical sculpture introduced to me by Matt DeVos, and originally by George Hart, I was finally graced with the opportunity to teach it to a group of keen teenagers. My students, who were participants in Math Camp at the University of Victoria, found the activity very engaging and a bit challenging.  In the one hour time slot, each of 16 students built a hexastix using approximately 48 3mm x 8cm coloured skewers, and they continued to work eagerly through their 30 minute break to expand their sculptures to about 72 skewers.

Producing high quality, colourful materials efficiently was the main challenge.  Three millimetre thick skewers do not come in 8cm lengths, but skewers typically fray when they are cut with a saw.  Efficient cutting was done with a stack paper cutter, like the one at All Image Printing, which cuts ten skewers at a time with little to no fraying, and very little time between precise cuts.  Rit Dye was used to colour the skewers.  It is not food safe, of course, but the bold colours are magnificent compared to results obtained with Kool-aid or food colouring.  Lastly, I provided small elastics and white glue.

It takes just under one hour to get students started on the Hexastix, but managing a large group is not difficult because students help each other.  I did not have access to a data projector or document camera.  I am still working on producing an instruction booklet for hexastix, however, I more or less followed the method in a video I made a few months ago (below, using toothpicks rather than skewers).  I emphasized that each colour represents a direction, and it is important to be able to identify, at first, the first colour that was added.  That colour has 7 sticks, which are separated by each other colour into sets of 2, 3, and 2 sticks (I made diagrams and showed them).  The most helpful type of diagram was one of the ends of the first colour sticks, showing the directions of the 2nd, 3rd and 4th colours, as they relate to the first.

The most difficult part is adding the first stick of the 4th colour, which is shown in the video, above.  I had to do this for most of the students, but if I had a data projector, or a prepared diagram or video, it would have been easier.

The Hexastix was a great ice breaker for math camp students, because they worked in groups to help each other interpret the instructions.  Mixing colours, and various options for shape and style allows for variety and innovation, while the Hexastix structure gives direction and, optionally, some mathematics to teach them.

I believe that the intersection of art and geometry is a great way to get many young people keen on math.  A point that is frequently ignored in the teaching of math at the pre-undergraduate level, is that higher math is in many ways a creative art.  We impose rhythm and such on music, and various other aesthetics on other creative arts.  In mathematics we impose logical rules, and try to find “nice”, and ever increasingly complex, statements that satisfy those rules.  Perhaps geometric art is the pop music of math.  It pleases our eyes, and sparks our curiosity.  It doesn’t just lead more people to want to learn more math, but it increases the appeal of math, garnering more allies for our cause.

It was reported to me that the students said building the hexastix was their

favourite activity at math camp this year.

Here is a video I posted on how to dismantle a pallet without splitting the wood (video).  I made a set of shelves with it and some recovered 2x4s.

Walking past the theatre yesterday, I saw they were showing

THOR 3D

I laughed out loud, and continued walking.  But thinking back over the last year or two, I can make the obvious  observation that every movie titled

<insert title here> 3D

is on the same intellectual plane as THOR 3D.  These movies are self-declared unintelligent!  Tough, perhaps THOR 3D deserves more Ds.  I propose this as a rating system for film festival lovers, and I think THOR 3D should be renamed to

THOR 10D

Recently I caught the geometric bug from Matt DeVos, when he showed an open faced icosahedron made of sticks and elastic bands.  Since then most of my free time has has been occupied by attempts to improve the icosahedron (the model of it, rather).  What began with a little model made of toothpicks and elastic bands, has evolved into hundreds of dollars in materials and tools, a special tool for making the icosahedron (and other shapes), and several sculptures.

The sculpture in this video, which is a bird feeder at the time of this writing, is three shapes in one.  The inner two are an icosahedron, which I built first, and a dodecahedron, which I attached to the edges of the icosahedron for support.  They are permanently fastened together, their inside is painted silver, and their respective outsides are painted red and black.  The outer icosahedron was built later, and then opened up to insert the dual pair.

I'm not sure what is going on with the optical illusion, but everyone I have shown the video to has trouble seeing that the outer and inner parts are often spinning in opposite directions, even when I'm in the shot moving them with my hands.

Enjoy the video.  Your comments and encouragements compel me to build more, and larger ones.

Last fall I made Tomoku into a book with 80 pen-and-paper puzzles based on the web game at http://tomokupuzzle.com.  Four months later I have not found a market for it, and I am looking for the lessons I need to learn.

The book is professionally printed, and the instructions are brief.  Many people compliment me on the "look" of the thing.  But it only goes skin deep.

Some people read the instructions, and then demonstrate to me that they misunderstood everything I wrote down.  Tomoku is a puzzle I find very intuitive, and some people understand the rules perfectly.  Perhaps you can suggest some clarifications?  Here are the instructions as they appear in the book.

Those who understand the rules think the concept is interesting, but they aren't hooked by the game.  Why is sudoku interesting?  Or other logic games?

I still believe that the Tomoku players are out there, and either I have not found them yet, or I have not communicated with them correctly.  Perhaps the pen-and-paper format is not the right one?  Maybe it would do better as a mobile app or a physical board game.

I want to hear what you think!

Here are two videos explaining Tomoku, with instructions on making a game board for it.