Special snowflake

You can create:

• unique snowflakes
• your own ways of paper folding
• conjectures and theories about symmetry and 2d transformations - rotations and reflections

How?
A typical snowflake fold always passes through the center. You can experiment with different folds: the results are always beautiful! Some folds are easier than others. For example, it is easy to fold and fold again for four layers. It is trickier to make six or ten layers. Coffee filters or thin origami paper works well, but regular thin paper is good, too. Small nail scissors cut more accurately and are easier to use.

Make a word snowflake out of your name, because you are a special snowflake! Make sure all letters touch each other and the folded edges. Early experimental snowflakes often fall apart. Figure out how to prevent it by connecting everything to each other and to the right edges of your fold. There is software that makes word snowflakes. You can use it to see how to position words on the folded paper. You can also email your creations to friends and family, or insert them into your web pages as widgets, like the snowflake with the word "math" here.

My favorite part: opening the name snowflake and seeing the incredible symmetric complexity of the result.

Why?
Because this activity is artistic, lovable, joyful, hands-on, requires no writing, and is related to European traditions (winter holiday decorations) and Japanese traditions (kirigami).

As you go

• Can you predict the number of layers your snowflake will have? How?
• Once you open the snowflake, you can find two types of transformations in it: reflections and rotations. Find them in yours!
• Another way to think about the same beautiful effects: mirror and rotation symmetry!
• Where is multiplication? Do you see it?
• Take pictures of your snowflake collection and share with the multiplication study

Higher and deeper

• Abstract algebra studies symmetry groups based on rotations and reflections.
• Geometry and trigonometry deals with angles you produce as you fold paper.
• If you keep doing the same fold (e.g. in two, again in two, again in two) you will be working with powers of that number.

This is a video of using angle measurements to make a ten-layer fold. In practice, most people just estimate their folds, instead of measuring them out exactly.

Strewing and snippets

Making name snowflakes is a slower activity, but a quick abstract snowflake can be created in a couple of minutes for a quickie math snippet. To strew more math around the house, can decorate windows with snowflakes, make garlands, use them in collages and scrapbooking, or place them in front of cool lamps for beautiful shadow effects.

Created: December 6, 2008, 6:51 am, by
Last edit: May 19, 2009, 9:30 am, by ( Edit, History )
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