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Make a mathematically fashionable hat!

This is one of the 48 projects for our Instructables: Made In Your Mind (IMIYM) exhibition at the Children’s Museum of Houston showing from May 26, 2012 - November 4, 2012. Produced in partnership with Instructables, IMIYM is an exhibit where families work together to build different fun, toy-like projects that help construct knowledge and skills related to science, technology, engineering, and mathematics while instilling a “do-it-yourself” attitude in kids so they feel empowered to explore, tinker, and try to make things themselves. To learn more, check out the article here.

For this project, we based our instructions on the Cool Way to Make a Party Hat Instructable created by golics, but there may be others on Instructables that are also similar. Often, the materials and process for building our projects are designed for use with a large number of visitors (we see over 800,000 annually) and the need to ensure safety in a mostly non-facilitated environment. So, yes, many of these projects have room for improvement in both materials and methodology, which is PRECISELY what we want to encourage the kids to do. So please do share your ideas for improvement and modifications!

Step 1: What You Need

We are selective in our materials for cost, ease of use, and safety due to our high traffic (800,000 visitors annually). So, for our purposes, this design worked best. But you may have other ideas - please share!
  • 2 – 17½” x 22½” Paper (we purchase this in bulk from thepapermillstore.com, but you have to purchase a large number of sheets. For most people, I'd recommend getting some nice wrapping paper and cutting sheets to size - that's what we did for prototyping and one of our videos (see below).
  • Pencil
  • Ruler
  • Scissors
  • Stapler
  • Crayons/markers/other decorations

Here is a video we shot for our O Wow Moment series that uses the wrapping paper instead of the paper above:

Step 2: The Video

We offer optional video segments of each step for this project in the actual exhibit. Here is a compilation of all the steps.

Step 3: Step 1 - Basic Folds

For both pieces of paper: lay down a piece of paper horizontally (landscape). Fold the paper in half by bringing the left edge over to the right edge. Fold the paper in half again by bringing the bottom edge up to the top edge. Fold the left edge down to the bottom edge to create a triangle.

Step 4: Step 2 - Make the Brim

On one of the folded sheets, measure and mark 8 inches from the bottom left corner along the slanted edge and bottom edge of the paper. Draw an arc or curved line to connect the two points. Cut along the arc. Recycle the rest of the paper. Open the paper to the shape of a semi-circle or half-circle. You should see three crease lines meeting at a point in the center of the bottom edge. From the center point where three crease lines meet, draw a 4 inch line along each crease line. Cut along each line you just drew. Open up the paper into a circle shape. Draw a four inch line from the center along the two uncut crease lines. Cut along the lines you just drew.

Step 5: Step 3 - Making the Top

Switching to the other folded piece of paper, fold the bottom edge of the triangle flap to the slanted edge of the paper. Crease and unfold. Measure and make a mark at 4 inches from the lower left corner along the slanted and bottom edges. From the lower left corner, measure and make a mark at 6 inches along the crease line. Use the ruler to connect the top and bottom marks to the center mark. Cut along these lines to cut out a diamond shape. Recycle the rest of the paper.

Step 6: Step 4 - Assembly and Final Touches

Unfold the diamond into a star shape and place it on top of the circle paper in the center with the points of the star lined up with the flaps in the center of the circle. Staple the points of the star to the points on the flaps. Use crayons, markers, etc. to decorate your hat and wear it proudly!

This is a case of using mathematics to create fashion. Radial or rotational symmetry describes objects that have the same geometry when rotated around a center point. In nature, many flowers, starfish, and octopi have radial symmetry. The two pieces of the Symmetrical Party Hat also exhibit radial symmetry because of how they were folded before they were cut.

Now that you know the basics of making this hat, create your own! How could you make it bigger or smaller? What would happen if you change from an arc and diamond to other shapes? Please post pictures in comments on what you make.

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