You'll no longer be sitting beside that sexy marine biologist dressed up as a sea anemone wishing that you could have a research themed costume too.

Finally, there is a combinatorics themed halloween costume!  Sport this beautiful Arduino and LED based rendition of Cool-lex combinations (research by Aaron Williams and Frank Ruskey), and show off your nerd times 2.

Here is the technical stuff on the combinations:

http://webhome.cs.uvic.ca/~ruskey/Publications/Coollex/Coollex.html

I used adafruit's LDP6803 LEDs.  There are tutorials on how to use them on that page.

This week I had the pleasure of teaching a Hexastix workshop to a group of volunteer mathematics educators, at the invitation of the 2011 PIMS Education Prize winner, Veselin Jungic. As with my previous experience teaching Hexastix at Math Camp, these beautiful mathematical objects will be the take-home project for students participating in Small Number, a program for First Nations math education.

Small Number is not precisely the name of the program, but of the protagonist in the associated animation, which is narrated in Blackfoot, Cree, and English on YouTube (embedded below). If you have never heard Blackfoot or Cree, I strongly suggest you listen to those versions. The languages are moving and sounds fascinating. Here is a language map, just to give you an idea of how many First Nations languages there are in British Columbia (I’m as amazed as you are!).

The animation and the school workshop program are products of several meetings at the Banff International Research Station beginning in November 2006. There, First Nations communities have partnered with math educators to assess the performance of First Nations students in mathematics, and to find ways of providing them with more opportunities to learn it. The data presented at the workshop shows, for example, that “Over the last seven years, only 5-7 percent of Aboriginal students have written and passed the Principles of Mathematics 12 provincial exam, compared to 25-27 percent of non-Aboriginal students.”

My part is to provide the program with 15,000 coloured sticks, as well as other materials, and teach their volunteers how to make Hexastix. I used my blog post about it as a visual guide to my workshop. The volunteers were challenged, and they enjoyed themselves. Here are some pictures of our workshop. (They were in a Picasa slideshow, which no longer exists.)

My first real math course - real analysis, in my case - was given by Dr. Jungic in 2004. His other students and I like to recall how he explained infinitesimals by saying “small small small small”, and motioning with his hands, and then he would describe large numbers by saying “HUGE” and throwing up his hands.

I invited some friends over to make icosahedrons in my workshop!  Here are the pictures. (They were in a Picasa slideshow, which no longer exists.)

After eating some delicious apple butter bars, cookies, and drinking chinese tea, we headed out to the studio where I helped my friends make these awesome cool geometric shapes.  The colouring of these icosahedrons is quite special, and soon I'd like to do a feature on that too!

Do you like fog machines?  Do you like fog machines that can go in your pocket?

That is what an e-cigarette is.  A fog machine that produces fog when you suck on it.  The "e-liquid" is actually the same, or a very similar chemical to the one found in fog machines.  And they work the same way (save for the sucking).  Current is delivered to a resistance heating wire that is in contact with the chemical.  The chemical then vapourizes and makes the fog.

I have converted the e-cig cartridge so that it draws power from a wall wart power adaptor, and is activated by a button.  With a good battery, you could have one of these in your coat pocket!

Here is some info on it:

 

Basic pushbutton switch circuit.

Greensmoke E-cig cartridge refilled with vegetable glycerin.  Inside it, a wire gets red hot, and vapourizes the glycerin.

Solder wires on instead of battery.

Don't hack adaptors that you use for other things.  You are very likely to break burn them out or otherwise destroy them.  Read the output in volts and in mA.  A smoke machine uses heat, which means high amperage.  These adaptors are less common.

Adaptor output MUST deliver at least 2 Amps and at most 4.5 volts.  If not, this is like short circuiting it and could destroy it.

Do not use a switch that stays on - you could cause a fire.

Here is the video:

 

Here is a picture:

How to make a Hexastix, like George Hart’s “72 pencils”.

Shoutout to Matt Parker’s standupmaths fans!##

Say hi in the comments if you came here from Matt’s video!

About Hexastix:

If you haven’t seen George Hart’s sculptures before, you need to go check him out: http://www.georgehart.com/sculpture/pencils.html .  And while you are at it, go see his daughter’s site too, vihart.com .  Hexastix, and this method of construction, were introduced to me by Matt DeVos, a mathematician at Simon Fraser University.  The word hexastix refers to infinitely regular hexagonal prisms - hexagonal sticks.  The idea is that if you filled every hole in this configuration, and expanded your Hexastix forever, the result fills 75% of space (I think), and has some crazy symmetry group described in “The Symmetry of Things”, by Conway, Burgiel, and Goodman-Strauss.

They are challenging at first, but easy once you get the hang of it.  Hexastix make great ornaments and gifts! Here are a few that I have made:

And here are the rest of them…

Your sticks and elastics might differ a little from mine.  This video will also help:

Materials :

1. A supply of sticks in 4 colours.  This hexastix uses 18 sticks of each colour, but you need a few extras for breakage and stuff.
2. 8 small elastics.
3. A poker thingy, like a pointed skewer.
4. (optional, not shown) white glue, water, ziplock bag, human powered centrifuge.

Fasten 7 orange sticks together with an elastic at each end.  I double my elastics so they stay on, but aren’t tight.

Now add four blue sticks

The blue sticks go between the orange ones, separating orange into sets of 2, 3, 2.  Fasten the blue sticks together with doubled elastics at each end.

Add four purple sticks

The blue sticks separated the orange ones into a 2,3,2 configuration.  The purple sticks will do that too, but in a different direction.  The old 2,3,2 separation is shown with blue lines, and the new 2,3,2 separation (by purple) is shown with black lines.

The purple sticks also go between the blue sticks, separating them into 2,2.

Here it is again from the ends of orange, and the ends of blue.

Put an elastic around each end of purple.

This is the key step.

Look down the end of orange and identify the 2,3,2 separations.  One of them has blue sticks between the sets, another has purple sticks, and there is one more, shown in white, with no sticks separating the sets of 2,3,2. There is one more way to split the orange sticks into sets of 2,3,2, and that is what the pink sticks do.

The pink sticks need to alternate properly with blues, and purples too, so there is a trick to inserting them.   Rotate the above configuration away from you, so that you now hold orange vertically, looking down the future pink direction.  Put your thumbs on the ends of the blue and purple sticks nearest you, and your middle fingers on the bottom end of orange.  Pull orange toward you, and push down on the blue and purple sticks. This should reveal six-sided holes for inserting pink!

Insert 7 pink sticks into the holes.  It does not matter which holes you choose, and it’s OK that some holes are open on one side.  Make sure that all pink sticks are parallel to each other.

Put elastics around the ends of pink.

Complete the blue and purple colours by adding three of each stick.

To add a blue stick, tuck it under the elastic, and push it into a hole.  As long as it is parallel to the other blues, it is in a valid hole.  You need to lift the elastic on the other end with a skewer to tuck the stick under that one too.

Here is the finished blue.  Some blue sticks are not really in “holes”, but that’s OK because they are held in place by the elastics.

After you have done the same thing with purple, you have constructed a Level 1 Hexastix.  Congratulations!

Expand it, starting with blue.  You need about 6 blue sticks.  The end of blue forms a hexagon, and you will expand it starting with the corners.  Locate the hole that is straight out and nearest each corner.  Notice that there are two corners that cannot be expanded (marked with x).  This always happens with the first colour or two that we expand, and can be fixed later.

Again, tuck the blue stick under the elastic, push it through the hole, and use a skewer to lift the elastic at the other end.

Here is blue with the corners expanded.  Next, we expand the sides of blue.

Use extra sticks to build the sides of the hexagon, and then remove sticks from the middle, OR take them from the middle and move them to the outside.  Whatever is easiest for you.

Here is the expanded blue.  Notice that I have left the original “middle” blue stick.  It serves as a reference point later.  We will make blue into a regular hexagon after doing the other colours.

You might find a second colour that also can’t be expanded on every corner of the hexagon, like orange here.  Keep looking at other colours until you find one that can be expanded on every corner.

Expand the corners of pink with 6 sticks.

Expand the sides of pink and remove the inner sticks, except the middle one.

Expand orange and purple the same way.  As the Hexastix gets larger, you need to be careful that the sticks go under all elastics when you push them through.

When pink, orange, and purple have been expanded, go back and fix blue.

Congratulations! Your Hexastix is now Level 2.

Use the skewer to make your elastics single.  Don’t worry if you break an elastic.  Just replace it with a new one before removing any others.

Time to expand blue again.  And again, there are two places that cannot be expanded yet.

Now expand pink…

Expand orange and purple… Be careful to tuck those sticks UNDER all elastics.

If you need to justify the orange sticks, set the end of orange down on the table, and push the other colours down.  Don’t forget to fix blue after expanding all other colours!

When you cannot expand the Hexastix any more, remove the middle sticks of each colour

Congratulations! You now have a Level 3 Hexastix!

You can leave it this way if you want to, or you can glue it so that the elastics can be removed. If you leave it, keep it out of the sun so that the elastics don’t degrade so fast.

Optional stuff:

Mix water and white glue so that it is liquidy, but gluie, and put enough of it in a bag to coat the Hexastix.  Put the Hexastix in too.  Seal the bag and shake it by cupping the Hexastix carefully in your hands.  Don’t hit anything with it, or your Hexastix could fall apart!  The Hexastix should be coated in glue.

To remove the excess glue, put the Hexastix into a container that you will spin around yourself with a rope.  I’ve used a milk jug, with a rope tied to the handle.  You can also use an old towel, by holding the four corners. Do the spinning outside, because if you hit something with the Hexastix, it can break.

Make sure there isn’t too much glue under the elastics, because this will make a little mark when it dries.  Wipe them with a Q-tip if you really want a nice finish.

When the glue dries, remove the elastics.  Be careful here: if you remove them too soon, your Hexastix falls apart and you can’t really fix it because it is clogged with glue, and if you wait too long, your elastics might get stuck.  I waited about 12 hours, and the elastics came off but the Hexastix was fragile.  If the elastics left a mark that you don’t like, you can do another coat of glue, or acrylic medium (available from art supply stores).  Make sure it is extra dry before applying a second coat.  The shaking could dislodge a stick if it isn’t dry.

The process is the same for glue-water and acrylic, except that the acrylic medium will make bubbles which you must remove by blowing sharply on them.  Here is the finish after applying one coat of glue, and one coat of acrylic medium.

FIN!