Radial/Rotational Recomposition: Drawing Π Through Rotation

*This is my first ever Instructables!

In this project, I explore the concept of rotational recomposition. - The process of where seemingly chaotic shapes are rotated and traced to reconstruct and reveal a recognizable image. In this case, the symbol π.

Along the way, I learned some new maths and brought it to life by modeling and 3d printing the design. There is just something about transforming something seemingly chaotic into a surprising order. Kind of like how pi itself is an infinite, irrational number, yet it still shows up in the most elegant places in maths, geometry, etc.

3d printer

I start by creating the shape of the thing I want to be projected. In this case Pi! I then break up the shape into different smaller segments to be placed upon the disc. Via rotation and extrude tool (cutting). I used some math to help me with the distribution of the segments so that it can be reconstructed correctly. However if you want to make something similar trial and error is also an option.

The design is sent to the 3d printer and printed. :)

Here I map the different segments to the respected angle of rotation for reconstruction. Numbering each piece with their respected angle. This step can of course also be done on computer, but I wanted to do it physically because I was bored.

I then add the angles as groove on the design for easier marking and aesthetics. However, did not add numbers to the angles or the shapes because my printer's printing resolution is very bad (it would just come out as a blob). Also when marking it follow the picture below to match the angle with the segemented shape.

Put a pencil, pen, or anything to keep the pivot point of the circle fixed. Mark a point anywhere on the paper on the circumference of the print. Align the respective angle on the circumference of the print with the marked point. then trace or color the segmented shape on the print with the same number as the angle. Repeat this until you have done it with all the angles/shapes. Then tadah! Out of nowhere, a pi has appeared.