Snowflakes

Of course there should be no December without lessons or mentions of snowflake and mathematics. I think snowflakes are some of the most beautiful natural objects for December. The patterns, the symmetry, the uniqueness, everything makes me excited and happy to learn more, to find more.

But fore today I have decided to talk about a special type of snowflake:  Koch Snowflake. This is a pattern which could give a small introduction to one of my favorite topics, fractals. As explained in mathwire.com, to start drawing this pattern you need to:

The Koch snowflake begins with an equilateral triangle.   The first iteration divides each side of the triangle into thirds, removes the middle third and replaces it with two line segments of the same length.   Students might visualize this as constructing a smaller equilateral triangle on the middle third, then removing the original middle third line segment.   Students can construct the first couple of iterations with pencil, paper and a ruler for measuring and marking each side into thirds.

I believe that this activity can offer much in terms of properties of triangles and there are many discussions that can be opened while doing this activity to revise some facts about equilateral triangles. And I believe that after this letting the children play and make it more colorful or use the pattern on different artistically projects is such a lovely thing.

After the idea of drawing the pattern, I believe there are quite some interesting ideas on finding the area. This could be an application for the more experienced students because they would need to use the concept of infinity. But also, I find it interesting to try with beginners especially for practicing the area of a triangle and then start a discussion on what they think it would happen after more and more iterations. For the mathematical calculations on this idea, I recommend the article Area of a Koch Snowflake.

And what about trying the inverse activity? What about instead of adding triangles, they need to subtract them? The shape would look very different, but what about the are? This could be some interesting food for mind ^_^

Enjoy. If you are a teacher let me know if you tried any activity, or if you are just a learner let me know what you think about this. Hope you all had a great day. I will let you enjoy some interesting objects made using the Koch snowflake:

SONY DSC

SONY DSC

Thank you for your help and support. You can find me on Facebook,  Tumblr,  Google+,  Twitter,Instagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!