University of Arizona
Institute for Mathematics and Education

September 14, 2010

Mathematics Symmetry & Beauty in Origami. presented by Dr. Brie Finegold


Origami provides a wonderful medium for exploring symmetries and properties within squares. Brie directed us to begin by determining a way to "construct" an equilateral triangle within the square piece of origami paper by creating just one fold at a time. After much exploration, alternative methods for creating an equilateral triangle were shared and a new problem was posed. Is the equilateral triangle whose sides are congruent to the sides of the square the largest equilateral triangle that can be created in the square? I'm not telling the answer.

Our next quest was to create a "belt" of smaller equilateral triangles, again using one fold at a time. After considerable exploration, alternative methods were presented.

After dinner, we were challenged to determine a method for creating a tetrahedron that had triangular folds in a structure that held its form. We were eager to have this quest resolved & resorted to using a youtube video teach us a method.

Click here for a copy of Brie's slides.

Click here to access a YouTube video to create a tetrahedron.


This evening's mathematical adventures addressed numerous performance and process standards were utilized in the presentation. Some of these include:

  • M08-S4C1-02 Predict results of combining, subdividing, and changing shapes of plane figures and solids.
  • MHS-S4C1-02 Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations and create 2-dimensional representations for the surfaces of 3-dimensional objects.
  • MHS-S4C1-03 Create and analyze inductive and deductive arguments concerning geometric ideas and relationships.
  • M08-S4C1-03 Use proportional reasoning to determine congruence and similarity of triangles.
  • M07-S4C1-05 Identify corresponding parts of congruent figures.
  • MHS-S4C1-08 Prove similarity and congruence of triangles.
  • M07,08-S5C2-07 Make and test conjectures based on information collected from explorations and experiments.



    Brie Intro Patty Group
    Brie Finegold introduces the origami sessionPatty Manciet discovers a method for creating an equilateral triangle.A group explores the origami constructions.