## Paper Folding: How to Construct an Equiangular Triangle

Paper folding or origami can be used to create intricate and stunning designs.  In addition, paper folding can also be used to teach or learn mathematics. In this post, we use a square piece of paper to construct an equiangular triangle. After the construction, we prove that the triangle is equiangular.

Steps in Constructing an Equiangular Triangle

1. Cut a square piece of paper. For the sake of discussion, we label the square ABCD.

2. Fold at the center so that AB coincides with CD . Crease well, then unfold.

3. Select vertex and fold so that A falls on the center line and the crease passes through D. Unfold. » Read more

## Origami and Its Surprising and Stunning Applications

Last year, I shared to you about Professor Haga’s superb book on the mathematics of origami titled Origamics: Mathematical Explorations Through Paper Folding. Yesterday, I found the video below on Facebook about origami and its relationship to mathematics, as well as its numerous surprising applications. Watch and be amazed.

Sometimes, I want to believe that somehow everything is connected to everything else. Well, I think physicists already believe that.

## Wholemovement and The Art of Folding Circles

Last week, I discovered Wholemovement, an interesting origami site about folding circles. The site highlights the beauty of circles and exhibits variety of 3D shapes that can be constructed from it.

To those who want to try the basics, you can read how to fold circles. The page includes procedures on creating a sphere, a tetrahedron, an octahedron, and an icosahedron using a circle. You may also want to explore the Gallery page to view more complicated folds.

Paper folding is closely related to mathematics. We can consider creases as lines, and intersections as points. Folding papers emphasizes congruence, symmetry, and transformation.

To those who are interested in this topic, check out Professor Kazuo Haga’s book Origamics. It is an excellent resource on the mathematics of problem solving.

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