First Cycle
 Faculty of Engineering
 Computer Engineering (English)
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:
Year of Study
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Semester
Course Unit Code

Course Unit Title

Type of Course

Y

S

ECTS

CAS1061

Geometric Origami

Compulsory

2

3

3

In this course we will be making origami models and studying the underlying mathematics of these models. The design of this course is discovery based and open ended . That is, the inclass activities and assignments for this course will consist of open ended problems, so you will have a great deal of input into what topics we will cover in this course depending on what you discover and think about when solving this problems. This will most likely feel very different from other math courses that you’ve had in the past. Hopefully, it will be more fun and exciting this way; however, it may be slightly more frustrating until you get the hang of it. There will also be a strong group work component.
We will study connections between paper folding and topics in number theory, combinatorics, and geometry. In particular, this course will cover selected topics from:
Basic Geometry: How can we use geometry to analyze our models? How do the dimensions of our models relate to the size of paper that we use? How can we form a 30 degree angle? Can we trisect angles? How do we divide a piece of paper into perfect thirds? Topics in geometry include the Pythagorean Theorem, similar triangles, angles, and properties of parallel lines.
Polygons and Polyhedra: How can we use origami to construct polygons and polyhedra of a given number of sides. This will introduce us to modular origami where we use multiple pieces of paper to form interesting shapes. Mathematical topics include Euler’s formula, coloring theorems, Hamilton cycles, and Buckyball classification and edge coloring.
Flat Folding: How can we determine from the crease pattern alone if an origami pattern will fold flat? Partial answers include Maekawa's Theorem and Kawasaki's Theorem.
Origami, Plain and Simple by Robert Neale and Thomas Hull.
homeworks, in class activities, demonstration