trautw / 123d

Tease your brain with one, two and treedimensional objects

123d

Tease your brain with one, two and three dimensional objects.

The old Japanese art of origami uses paper to create beautiful objects. Folding is done along straight lines. This results in objects that have planar surfaces in the three dimensional space. A straight line (one dimensional) is used to divide a sheet of paper (two dimensional). Folding takes place there to create a three dimensional object having two planar sections.

Folding along curved lines gives new options but is much more complex. While exploring this I did some experiments. One beatiful result is a lamp shade shown here. When folding along curved lines (one dimensional) a sheet of paper (two dimensional) you immediately get a shape that has curved planes (three dimensional, not sections of two dimensional sections). Another interesting possibility is that folding can end within the plane. It looks like this technique opens very new possibilities.

It is currently unclear for me how this can be applied to folding higher dimensional objects. What I can see in the three dimensions is that it is possible to fold along lines (one dimensional) and as a result have places getting in contact (tree dimensional) that are far apart on the paper (two dimensions). A two dimensional person could use this trick to travel to distant places of the paper with no speed limit. It can travel faster than the speed of light.