Pi Coin (Origami)

Hi, I'm David Tapias, I'm an origami folder and creator.

When I saw this challenge, I started thinking of ideas like creating a model that starts with a circle, or maybe something modular using circular shapes. But then I remembered a new and interesting technique that has emerged in recent years for designing origami models. The idea is to play with the two colors of the bicolor papers in 2D, almost like “painting”, the contour of each model are geometric shapes such as hexagon or octagon, which can near to the circle shape. That’s why the technique has been named Origami Coins or Pictoric Origami.

So, I thought, folding an octagon with the Pi symbol inside could be a great idea, especially because the octagon also has historical ties to the calculation of Pi, as used by Archimedes.

The origamist who introduced this technique was the Chinese artist Simple Origami (@simpleorigami094). While exploring some of his models, I noticed they often share a base. I used that base and began folding and folding, trying to create the symbol for Pi and here I will teach you my result.

1. 1 square bicolor paper (20cm x 20cm)
2. Glue Stick (optional)

In origami, there are two basic folds, and these folds are the foundation for making any origami model. The first fold is called the valley fold, and it is represented by blue lines (like rivers). The second fold is called the mountain fold, and it is represented by red dots and lines (like lava from a volcano). Check the image.

In some steps, I will talk to you about these folds, and some photos will include these lines.

I will use a square with colors orange and yellow, and the background will be orange and the symbol of pi will be yellow.

Fold as shown (those folds are Valley folds)

When you fold two sides to the diagonal crease, you are folding a typical base in origami, the kite base.

Repeat the kite base using the three missing corners.

Turn over and identify the octagon, mark the octagon as shown.

Turn over and make the valleys fold as shown. After the paper will start to close counterclockwise. Close the figure as shown on the last image. (That is the figure base that I told you on the introduction).

Unfold to fold all tips as clockwise. We have four long tips and four short tips.

Fold the long tip and short tip as shown.

Fold the long tip as shown. About origami, this type of fold is called, squash fold.

In this step, you must change the crease existing as mountain fold to valley fold, and the valley fold to a mountain fold on two sides.

Open all tips to hide the long tip that we are working, hide until background.

Important: This is our reference position for folding the model. So, if you need to rotate it to make a fold, once you're done, always return to this original position. The tip of the long flap that we hid should always be pointing upward.

Lower the two long tips as shown.

Lower the short tips as shown, you should have the two short tips at the bottom. Move the long tip to the rigth.

Open the layer as shown to fold horizzontally, the point of reference to stopt to folding will be the color change when you are folding up. The sides of the paper will lif up, flatten as shown.

Unfold up to step 17, fold the long tip to the left and repeat the step17.

Using the existing creases, the paper will have tension on the long tip. Push the long tip to reverse that point, as shown.

Fold and unfold as shown.

Open the layer and fold as shown, remember, the main reference to fold is the color change. Flatten the tip as shown.

Repeat the step 21 on the other side. Unfold to where shown.

Now, you must making an outside reverse fold with the orange triangle, we have all creases, so the paper should pull towards those folds. Open the layers as shown to make most easy the folds and avoid breaking the paper.

Open the layer and making the valley fold as shown. Unfold.

Using the existing creases, the paper will have tension on the long tip. Push the long tip to reverse that point, as shown. The yellow color on the little triangle, it will must hidden fully.

Repeat on the other side the steps 20 to 25.

Using the existing creases, fold the short tip as shown, After, inside reverse fold to hide.

Fold the long tip to the left, open the layer and you can see a triangle, fold the triangle to trap the layer as shown

Fold as shown, The image 6 is showing a rrabbit ear fold but on mountain fold. The size of the left long tip is a little bit major, so you should making a little fold to adjust that. The little extra mountain fold is shown inside the circle.

Fold as shown, the fold has not reference. After, unfold.

Using the references to the last folds, fold a valley fold, after using the existing creases fold again as shown.

Fold the valley fold having as a reference the base the "Foot right"

Valley fold, note that the crease underneath starts at the tip of the triangle. Now you have a little triangle that is visible to the front. Use that triangle to trap the "foot left" insert them in the pocket as shown.

Mountain fold to hide the tip as shown.

Repeat as the step 33.

You’ve finished the Pi coin, but maybe you used traditional paper and noticed the figure opening up.

This happens because this type of origami builds up front layers.

In the world of origami, we use many types of paper, and for this kind of model, it’s always recommended to use sandwich paper.

To make sandwich paper, we use: thin paper + aluminum foil + thin paper.

If you want to learn how to make this type of paper, you can visit my website ( click here ) I have a tutorial for it.

The second image shows a Pi coin made with sandwich paper (12cm x 12cm). The figure uses no glue, and the result is perfect.

One rule for considering a figure as true origami is the fact that no glue is used in its creation.

However, there are cases where the paper design may be perfect in terms of color or texture, but its thickness is not ideal causing the figure to open up easily.

This stage is considered the finalization or finishing of the model, and in such cases, there’s no choice but to use glue.

If that’s your situation after completing the model, use a glue stick, as it doesn’t add much moisture.

Apply glue as shown.

Congrats !!! You completed the model.

If you want know more about origami, you can visit my web page (click here).

Thanks for fold :) .