#MathArtChallenge 97: Tomoko Fusé’s Bird Tetrahedron Origami

The Challenge: Make an origami sculpture using Tomoko Fusé’s text Multidimensional Transoformations Unit Orgiami. (I used instructions on pgs 134, 138-139.)

Materials Needed: Paper (origami paper is handy, but any paper will work) and scissors/paper cutter.
Math Concepts: 3 dimensional building, angles, space filling, rotations, proportions

I love this particular type of origami because you get to determine the shape and scope of the final piece. You’ve basically made yourself some origami legos. If you have a lot of time, you’ll be able to fill space (well, there’ll be holes) with this unit & connectors, and could therefore, theoretically build a really dramatic sculpture, much like one could also do with legos. Just this is with paper!
For mine, I opted for the relatively simple tripe helix with a double rainbow. It took about 8 hours of folding and construction. We’re all a ways a way from this, but someday, post-pandemic, this would be a REALLY lovely project to do as a whole class or in groups.

To build this sculpture, you need square paper, scissors and 3 different folds:

  • Bird tetrahedron (technically a di-triangular pyramid)
    • 3 pieces of nxn square paper per di-triangular pyramid.
  • Horizontal connectors.
    • If your bird units are made with nxn paper, these are n/4 x n/2 paper. (1/8th the area of the nxn paper) 2 connectors needed to connect each 2 bird units. 6 needed to connect 3 units.
  • Vertical connectors.
    • If your bird units are made with nxn paper, these are n/2 squares. (or 1/4th of the original nxn paper) 3 connectors will connect 2 bird units.

Folding the bird units:

Putting the bird units together:

Folding the horizontal connectors:

Putting bird units together horizontally:

Folding the vertical connectors:

Putting bird units together vertically:

Questions to consider:

  • What forms are possible? What are excluded?
  • How much space is actually taken up?
  • Is it possible to get a square grid going here? A cubic one?
  • How many transformations are actually happening?
  • How many triangles appear in each of the tetrahedral units?
    • Each di-pyramid is actually 3 square faces folded along their diagonal to make 2 45-45-90 triangles. What do you notice about that construction? What might it tell you about the angles between the faces?

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

6.) Attend to precision. (This gets pretty annoying if you’re not at least working toward being precise when folding.)

7.) Look for and make use of structure. How can these units be put together? What is possible and what is not?

8.) Look for and express regularity in repeated reasoning What do you notice about how the pieces do and do not fit together? What generalities can we determine?

#MathArtChallenge Day 20: Origami Icosahedron

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

THE CHALLENGE: Fold 30 identical pieces of paper to put together as an icosahedron.

Day20 Icosahedron

MATERIALS NEEDED: 30 square pieces of paper. No problem if it’s not origami paper, you can use regular paper (and you can decorate it if you want!)

#MathArtChallenge Day 12: DRAGONS

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

PROPS TO: Kate Nowak who suggested this.

THE CHALLENGE: Create as many iterations of the Dragon Fractal as you can. See below for my attempts and videos to help.

MATERIALS NEEDED: There are a couple options here.

  1. Paper and marker (sharpie?). Maybe grid paper, preferably paper that is thin enough to see through (notebook paper is normally thin enough)
  2. Strips of paper to fold it.
  3. Whiteboard marker and whiteboard/window?
  4. ??? I bet you have better ideas than I do.

Here are my attempts:

And below are videos explaining what it is and how you can make it, too!

#MathArtChallenge 9: Comparing Origami Butterflies

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

2020-03-24 08.18.24

THE CHALLENGE: Make two different sizes of origami butterflies and then see what you notice and wonder about your pieces!

MATERIALS NEEDED: Two different sizes of square paper. (Can be obtained from non-square paper if you ask nicely.)

Instructions below.

Day9 MAC origami instructions

#MathArtChallenge Day 4: Hyperbolic Geometry

Day4 MAC hyperbolic planes

THE CHALLENGE: Fold your very own Hyperbolic Plane from a simple piece of paper!

Materials Needed: A square piece of paper. Youtube instructional video below!
Math Concepts: Hyperbolic planes, vertices, opposites, exponential functions, reflections, symmetry

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

4.) Model with mathematics Compare this model to a surface with positive curvature (a ball) or zero curvature (a piece of paper) surfaces. This surface has negative curvature. What do you notice about the 3 types of curvature? What’s the same? What’s different? What can you do on this surface that you can/cannot do with the others?

5.) Use appropriate tools strategically. As you’re folding this, discuss with students what tools make the folding easier or less easy. What kinds of paper works best? What sizes?

6.) Attend to precision. Discuss with students how successful your models are depending on the precision of your folds.