Topology Mathematical Tree Ornament

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Want to tie in some Mathematics with your DIY Christmas decorations?  These are so fun, so simple, and quite honestly, so addicting to create.  Give your students or children a stack of 5" X 5" pieces of paper, and have them cut to their heart's content.  Try to find either foil origami paper, velvet sheets of scrapbook paper, or even construction paper to make these fun and educational ornaments.

You may be asking yourself, "What is topography?"  Well, basically topology is the study of continuity and connectivity.  For instance, if you have an object (like a circle) that is manipulated in such a way to change its shape...twisting, stretching, rearranging (and so becomes an ellipse), the properties of this object are still the same; they don't change. Cutting an object to change the shape of it is allowed, but tearing is not.  If you want to dig deeper into the study of topology, visit mathworld.wolfram.com for more information.

Here are the simple instructions:

You can free hand your circle, but why do that when you can give your students valuable practice using their compass? :)

Cut out the circle.

The first fold. 

The second fold. 

Now, for the first cut.  Cut a curved line, starting at the right.  Be sure to not cut all the way through. 

Turn it upside down and cut again, from the other direction.  Again, be sure to not cut all the way through. 

Continue cutting curved lines almost all the way through, alternating sides, until you reach the end of the paper. 

Now, unfold the paper. 

It's super fun to stretch it out to see all the layers of the "once-confined circle". 

Attach an ornament hanger from the top and decorate your tree with many beautiful topography ornaments!