A uncut piece af paper can be formed in a three-dimensional shape. Straight folds and curved folds will change the basIc shaping variations that already exist.

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### What options do you get when you take a piece of paper and move it in one big swoop in 3d?

- The paper is bent and ultimately forms a tube.
- It rotates around a point and forms a cone.
- Two sites of the paper are rotated in opposite directions, a spiral is formed. Smaller strips of paper can form more rotations than wider strips, with the same length of paper.

### Now let’s compare a straight fold with a curved fold.

- The straight fold divides the paper in two parts (faces).
- The shape becomes tree dimensional. The height increases. On the ground level, the width decreases.
- When the faces lay on top of each other the thickness doubles.
- The fold is ridgid but when the two faces lay flat on top of each other, the fold will bend.

- The curved fold.The height increases. On the ground level, the width decreases. Where the shape is higher, the width is smaller.
- Two opposite sites of the paper can not stand flat on the table.
- The fold can bend.
- The curved fold also divides the paper into two parts, but they can not lay flat on top of each other.

The image above shows a combination of a strait fold and a curved fold.

### Folded objects

In 1927-1928 Josef Albers thought a preliminary course: paper study at “das Bauhaus” in Weimar. The hyperbolic parabola was one of the objects that were folded.

Origami Hyperbolic Parabola Instructions

This “Ellipse with 10 flaps” was designed(or invented) by Jun Mitani.

crease pattern

Can you tell what information on this page is relevant for the shapes of these object?