3 Dimensional Snowflakes.

One of the sessions I attended at the Educational Conference was on 3 dimensional printing. It was awesome because I learned a bit about the math involved in creating the snowflake to the left.

I created it in a free online program called Blockscad.  Fortunately, the person leading the session walked us through the process step by step so we'd get  a proper result. 

I will tell you I forgot to pick up my finished product, otherwise I would show it to you via photograph.

To the right, you see the code we wrote for the snowflake.  Basically, I had to give the number of shapes which in this case is a square, I needed to produce the final product.  Then I had to find the angle rotation for each square by taking 360 divided by the number of shapes.  So this would be 360/10 or 36 degrees.

That is what the two brown ones did.  The purple tells the computer to go from 0 to 360 using a jump of 36 degrees.  You have to tell the computer how much to rotate the figures and move them. 

Immediately, you have a real life use of transformations in a situation students might actually relate to especially if they know they can print the final product once its done.  The instructor had us create a square by finding the difference between two cubes so only the x and y coordinates actually had the difference while the z coordinate has to be zeroed out.  As far as I can tell, the difference in the x and y axis gives the thickness of the line. 

It was fascinating to play around with the rotation and translations because one controls the distance between the "floor" and the top of the snow flake while the other sort of changed the flatness and created more depth.

If I had not had something to follow, it would have taken me a while to actually figure everything out.  As I worked this, I got to thinking how much fun it might be to do this as an art project where they students start with the square and have to create their own unique snowflake.  Imagine having them determine how far to move the square each time. 

I'm off to write a lesson for my geometry class based on this type of activity.  I love attending conferences because I end up with lots of new knowledge and ideas for my classes.  Let me know what you think, I'd love to hear. 

Have a great weekend. I'll be spending it watching hula, hula, and more hula.  Let me know what you think. I'd love to hear.