Origami Quilt Squares at Math-on-a-Stick

I sure did not. But now I do.

I learned this particular mathy art from @RosieL52 during a math art club arranged over the summer by Siddhi Desai, Shraddha Shirude & Jenn White. She learned it from the book Extreme Origami by Kunihiro Kasahara.

To make these, you start with the pinwheel base. You can look up many, many tutorials for “origami pinwheel base” and I’ve made a quick video below (no sound). Then… just start folding. It helps if you keep your folds working in 4-fold symmetry (do the same to all 4 squares made by the pinwheel base), but I sure won’t discourage you from trying other things.

Lots of examples below that you can create through experimenting. One of the things I liked today about the kids who stopped by the Math-on-a-Stick booth was that a lot of them would immediately know what they wanted to try after they got the pinwheel base done. Mostly, you figure these out with experiments. Try folding up. Try folding down. Can you make squares? How about a kite? Fold forward. Fold backward… Everything goes, and if you mess it up, well, I bet you can get a hold of more paper. By all means, try recreating some of the images below.

#MathArtChallenge 100: Balloon Polyhedra

In the first, allow me to thank each and every one of you who has participated in the #MathArtChallenge in the last few months. This is my “last” post. Meaning, I don’t promise to make more Math Art Challenges, but there’s always the chance that something will come up…

All of the #MathArtChallenge-s will continue to be up on this blog, and I really hope that you’ll make use of them in your classes or in your fun time or however brings you joy.

The Challenge: Today, you get Balloon Polyhedra. There’s actually several papers written about this, so go check them out.

Materials needed: Twisting balloons, pump, patience
Math concepts you could explore with this challenge: angles, arithmetics, counting, geometry, graph theory, polygons, polyhedra, symmetry, vertices/intersections

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#MathArtChallenge 99: Quilts & the Underground Railroad

A quilt containing 6 of the blocks mentioned below as having possibly been used as a code in the underground railroad.

The Challenge: Learn a bit about the code discussed below, and then have yourself or students create some or all of the quilt blocks discussed.

Materials needed: Certainly you can make these as actual quilt pieces. You can also just use a square piece of paper and work on construction within that using paper and pencil.
Math concepts you could explore with this challenge: angles, arithmetic, geometry, philosophy on math, polygons, symmetry, tessellations.

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#MathArtChallenge 98: The Most Beautiful Proof

A blue watercolor with gold lines and highlighting.

The Challenge: Pick YOUR favorite proof, or mathematical fact and illustrate it. What’s beautiful about it? Why do you love it? I really, truly want to know.

Materials Needed: Really depends on your pick!
Math concepts you could explore with this challenge: Philosophy on Math. Mathematical communication.

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#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

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#MathArtChallenge 96: Not so much rational tangles as… a 2 link challenge.

2 link knots
A grid arrangement of a variety of green and teal crocheted links.

The Challenge: How many 2 link knots can you find? See the examples above to help you get started.

Materials Needed: knot materials (these could be crocheted like I have, or shoe laces, or electrical cords which you can plug into themselves)
Math concepts you could explore with this challenge: combinations & permutations, graph theory, knot theory, topology, vertices/intersections.

Continue reading “#MathArtChallenge 96: Not so much rational tangles as… a 2 link challenge.”

#MathArtChallenge 95: Magic Squares

Overhead view of lego towers arranged in a 3×3 grid.

The Challenge: Create a magic square. Bonus points if you make it a physical thing.

Materials Needed: Legos, blocks or coins all work well for making these towers. Could also be pen/pencil & paper, of course.
Math Concepts: Algebra, arithmetic, counting, proportions/ratios, structure, sum of 1-n integers

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#MathArtChallenge 94: Twelvefold Islamic Geometric Rosette from Samira Mian

12fold rosette full

The Challenge: Make yourself a 12-fold Islamic Geometric Rosette.

Materials needed: Compass, straight edge, paper, pencil, colors
Math Concept: angles, circles, geometric construction, geometry, Islamic geometry, lines, polygons, symmetry, tessellations, vertices/intersections.

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#MathArtChallenge 93: Archimedean Solids from Vertex descriptions


The Challenge: Using a vertex description, build yourself one, two… up to all 13 of the Archimedean solids.

Materials needed: Card stock and tape (painter’s tape is great, or masking. Other stuff will work, but I’ve had more success with the paper-y tapes.) OR Magnatiles, but those can get pretty pricey.
Math Concepts: structure, polyhedra, angles, 3D structure

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#MathArtChallenge 92: W.E.B. Du Bois Data Portraits

The Challenge: Following the style of W.E.B. Du Bois’ Data Portraits, update or create a graphic demonstrating current data. For example, below on the left is Du Bois’s portrait comparing Black and white occupations in 1890 and on the right is my recreation using the closest set of matching data I could find in 2018.

Materials Needed: Maybe graph paper, maybe simply regular paper and writing tools.
Math concepts you could explore with this challenge: Statistics

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