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Mathematics of Origami (Fall 2024)

This course introduces the mathematics of origami and origami design. It follows a flipped classroom format. Students complete assigned readings before each class, then participate in group discussions and problem-solving sessions during class time.

Coordinates #

Time: M 9:00AM - 10:00AM
Location: Wyman N425

Instructor #

Mateo Díaz (mateodd at jhu dot edu)

Grading system #

Grades will be based on two components: participation (60%) and a final project (40%).

Participation #

Students are expected to read before class and actively engage with the instructor and fellow students. Asking questions, suggesting potential solutions, and sharing thoughts during class are ways to engage.

Final project #

For the final project, students have three possibilities: (1) read a paper concerning Origami or a chapter from [O] (discuss with the instructor before choosing) and present it to class, (2) design an arbitrary origami figure and do a presentation about the design process and the decisions that it involved, (3) solve one of the challenges below and do a presentation about it.

Needless to say if you choose to do (2) or (3) you need to bring a physical folded figure to class.

Readings #

We will use two books:

A copy of [ODS] will be provided to each student (to be returned by the end of the semester). [O] can be accessed online by Hopkins students in this link.

Date Topic Reading
September 9 Introduction -
September 16 Basics: diagrams, crease patterns, and traditional basis ODS: 2, 4
September 23 Origami constructions O: 1.1, 1.2, 1.3
September 30 Axioms and solvability of equations O: 1.5, 2.1, 2.2
October 7 Splitting points and grafting ODS: 5, 6
October 14 Circle Packing ODS: 9
October 21 Molecules ODS: 10
October 28 Tree theory ODS: 11
November 4 Box pleating ODS: 12
November 11 When can a crease pattern be folded flat? O: 5.1, 5.2, 5.3, or This paper
November 18 Project discussion -
November 25 THANKSGIVING -
December 2 Final project presentations -

Challenges #

There exist many solutions for some of these challenges. Do not look them up, do it yourself!

  1. Design a Callinectes sapidus (Maryland blue crab) using a one square pice of paper.
  2. Design a Icterus galbula (Baltimore oriole) using one square piece of paper. Your figure must incorporate a “color change” to show the oriole’s distinctive orange/black patterns. Use paper that’s orange on one side and black on the other. The final design should display both colors to match the oriole’s appearance.
  3. Design a Cyanocitta cristata (Blue jay) using one square piece of paper. Just as with the previous challenge, your figure must incorporate a “color change” (white and blue).
  4. Design a “3D shadow” of a 4D hypercube (you can use modular origami).
  5. Design an origami modular for three intersecting golden rectangles.
  6. Design an origami tesselation (one square pice of paper) of at least two regular tessellations of the plane (one has to use hexagons).
  7. Design origami modulars for at least two of the Platonic solids.
  8. Design an origami modular of a polyhedral stellation.

Resources #

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