Paper is such a great medium. You can find it almost anywhere. With a couple of quick folds you can transform it from a fragile flat piece into a strong 3D object. Most people are familiar with origami, the art of folding paper – if not, learn more here with a Scholastic Origami Math lesson. But fewer people are familiar with modular origami, which is a technique that involves creating folded pieces that can be connected together to create larger 3D models. For example, you can fold a piece of paper like this to create one module:
and combine 6 modules to create a cube
or combine 12 modules to create an octahedron
or 30 modules to create an icosahedron.
Grab some thin paper and follow this Math Craft tutorial to create your own.
Want to learn more? Check out these resources:
You know what we love to build things with? Everyday objects, like popsicle sticks! Inexpensive, light-weight, and versatile, these are an easy way to construct a variety of things with tape or glue and can easily be decorated with marker, paper, or string. From bridges to buildings, creatures to words, you can really build almost anything with them. We like to get geeky and these materials and build mathematical sculptures. These are not only a great hands-on mathematical learning tool for exploring abstract concepts (physically scaffolding from 2D shapes to 3D forms), but can also become decorative sculptural lighting elements. Though you can make almost any angled shape or form with popsicle sticks, we recommend starting with building a cube first then working on building up to an icosahedron, which has 20 faces (each face is an equilateral triangle), 30 edges, and 12 vertices (5 edges meet at each vertex).
- (at least) 60 popsicle sticks
- hot glue gun
- hot glue sticks
- optional decorations, paper, transparency film, markers, buttons, string, etc.
- battery operated tea light
- Follow this great tutorial to build an icosahedron.
Design Experiment Considerations:
- Cover each face with different material and experiment with shadow play.
- Hypothesize how much strong it would take to wrap the entire sculpture.
Want to learn more? Check out these resources:
Photography is a great way to explore symmetry as it naturally exists around us, as well as a creative medium for generating your own symmetrical views. Symmetry is based on the mathematical principle that If you divide something in half either side is a mirror image. Check out more information and examples here: http://www.mathsisfun.com/geometry/symmetry-line-plane-shapes.html
Three-dimensional mathematical puzzles are a fun way to develop problem-solving and visual reasoning skills but they can also turn into beautiful works of art. Whether using everyday objects (such as popsicle sticks and straws), origami (paper folding), or kirigami (paper cutting), you can create something awesome while you also apply some cool math.
Check out our posts for some inspiration:
Everyone loves jewelry. Have you ever been admiring a piece of jewelry only to find yourself thinking, “if only it had [this]” or “I wish it was a different color” ? Now with affordable 3D printing processes, you can design your own wearable art in free 3D modeling software, such as TinkerCAD or Autodesk 123d Design. Then you can print your design out of plastic on an inexpensive 3D printer, such as the Printrbot Simple. Don’t have access to a printer? No problem! Upload your design to Shapeways and pay for materials and shipping costs. Here are some rings that our workshop participants have designed and printed:
- ratio and proportion
- negotiating balance in design and the 3d modeling plane
- Tinker with other people’s 3D designs
- Our favorite 3D Printer! Inexpensive, portable, and a workhorse.
Using the art of paper cutting (kirigami), you can transform multiple copies of 2D shapes (modules) into clever 3D objects by connecting or combining them in different ways. Mathematical sculptor/designer (and engineering professor), George Hart, uses this technique to create amazing mathematical puzzles constructed as sliceforms and slidetogethers. These sculptures are not only beautiful, but are also concrete physical explorations of abstract mathematical concepts that can address mathematical knowledge and visual reasoning skills. He has many publications that discuss this basics of modular kirigami (i.e. read this article that discusses an overview, create a “tunnel cube” out of a deck of cards) and he has great resources to help teachers integrate these concepts to “make math visible” in the classroom.
MAKE YOUR OWN MODULAR KIRIGAMI SCULPTURE
Based on Jessica Jones’ design, you can connect 12 identical copies of this simple flower piece to create a unique 3D flower sphere that is based on pentagons. No adhesive needed; the only ingredient is paper! We like to cut ours out on colorful cardstock paper using by duplicating the design in Silhouette Studio software and then cutting them out on our Silhouette Cameo machine. Then we turn them into jewelry, lampshades, and ornaments.
You can vary the design of the piece to create other unique designs too, such as this one that is based on the Loomi lampshade design:
WANT TO LEARN MORE? CHECK OUT THESE EDUCATIONAL EXTENSIONS
Learn more about the historical and cultural background of kirigami: For the Love of Paper (Prezi)