First Cycle - Faculty of Engineering - Computer Engineering (English)
Y : Year of Study S : Semester
Course Unit Code Course Unit Title Type of Course Y S ECTS
CAS1061 Geometric Origami Compulsory 2 3 3
Objectives of the Course
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 in-class 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.
Learning Outcomes
1 analyze crease paterns, find dimensions of crease lines and angles reviewing necessary geometry
2 identify Maekawa's Theorem and Kawasaki's Theorem
3 identify Euler’s formula, coloring theorems, Hamilton cycles, and Buckyball classification and edge coloring
4 use geometry to analyze models
5 connect paper folding and topics in number theory, combinatorics, and geometry
Mode of Delivery
Formal Education
Recommended Optional Programme Components
None
Course Contents
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.

Weekly Detailed Course Contents
Week Theoretical Practice Laboratory
1 Basic geometry and equilateral triangle activity Folded some origami models and analyze crease paterns, find dimensions of crease lines and angles reviewing necessary geometry (Pythagorean theorem, sin and cos, etc). Folded a box and determined how end dimensions related to starting dimension of paper. Started activity on how to fold an equilateral triangle.
2 more on equilateral triangle activity (maximal part) and fujimoto activity Worked on folding a larger (largest) equilateral triangle and verifying the triangles they folded were really equilateral (many were almost equilateral) and did Fujimoto approx technique for folding paper into nths. Took a lot of examples for them to fully understanding the Fujimoto technique
3 rediscussed how to fold 15 degrees and maximal equilateral triangle and did the number theory of fujimoto.
4 folding regular n-gons with fugimoto applied to angles from Mathematical Reflections
5 flat folding activity, part 1
6 trisecting angle activity and dividing equal thirds activity
7 more on flat folding, presentation 1
8 Midterm
9 Group presentations, more flat fold, modular unit folding made tetrahedron
10 more modular unit folding, made octahedron and hexahedron, euler’s formula, other V,E, F formulas, apply formulas to determine all regular polyhedra with trianglular faces, and PHiZZ unit activitiy
11 coloring question and crane activity Colored maps to come up with 4 color theorem. Colored flat foldable designs to discover only need two colors.
12 review, planar graphs activity, buckyballs activity part 1
13 buckyballs activity part 2
14 butterfly bomb activity, fun folds
15 fun math folds, parabola, hyperbolic paraboloid, miura map, wave, other fun folds
16 Final Exam Study
17 Final Exam
Recommended or Required Reading
Origami, Plain and Simple by Robert Neale and Thomas Hull.
Planned Learning Activities and Teaching Methods
homeworks, in class activities, demonstration
Assessment
AssessmentQuantityWeight
Term (or Year) Learning Activities60
End Of Term (or Year) Learning Activities40
Total100
Term (or Year) Learning ActivitiesQuantityWeight
Midterm Exam140
Homework Exam1060
Total100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Project Exam1100
Total100
Language of Instruction
Language Codes
Work Placement(s)
None
Workload Calculation
Activities Number Time (hours) Total Work Load (hours)
Theoretical 14 2 28
Midterm Preparation 1 3 3
Home Work 10 2 20
Project 1 20 20
Total 26 27 71
Contribution of Learning Outcomes to Programme Outcomes
PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9PO 10PO 11PO 12PO 13PO 14PO 15PO 16
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LO 20000000000000000
LO 30000000000000000
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LO 50000000000000000

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