Origami with Non-square Paper

I observed some origami creases and came up with the assumption: round paper can do the same job, but with less paper, and there are even more possibilities.

I originally planned to fold out the paper cranes. But when I faced a round piece of paper, I completely forgot how to start. This is a very strange feeling. Then I noticed that for the same crease, square paper can have two different results, but round paper has only one result.

Square origami seems to be easier, because line-to-line alignment is used for folding, while round paper requires using dots as a reference. Along with my self-doubt, I finished the paper crane with the round paper.

From this origami, I think my initial assumption was wrong. But I want to prove it wrong from another angle, so I did some analysis on the origami cp (crease patterns) diagram. I add a circle to the cp diagram I found online.

After comparing this picture with my actual origami, I found that they are different. In the actual folding, I intentionally modified some crease patterns to create acute angles and straight edges. From the results, the round paper cannot show the angles when folding the paper crane. The convex part in the middle of the paper crane is similar in size, but the round origami lacks corners, so the result of the square origami is more slender.

What if we avoid origami that emphasizes corners? With this question, I completed the following two origami.

The first one is a paper bag, while rounded edges make this origami easier to close and open.

The second one is an umbrella. Round paper can also be used to make paper umbrellas directly, while square paper needs to be cut into polygons.

In addition to square paper, rectangular paper is also widely used. Take the Sui’s sewing organizer bag I made earlier as an example, rectangular paper with an aspect ratio of 1: 2 is used many times.

Trapezoid paper based on rectangular paper can make some origami that is layered and deformable. Below is an origami toy I made this week.

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