My project of printing a sphere is ready to implement. I attached two diagrams, one for the front of the ball, one for the back. The purpose is to illustrate the difference between flat and curved space. It turns out that the distance metric on a ball can be derived just as easily from the straight tangent vector (cartesian coordinates) as it can from curved vectors in the surface of the ball (longitude and latitude coordinates). This sphere is intended to compare the two derivations.
This is a beta version. I plan on making improvements to the design. Obviously, the topic of curved space requires more than one sphere to explain it. My intention is to use the balls to liven up my living room and to provide concrete examples to show people of what otherwise is a theoretical topic. I plan on demoing them only to select relatives or friends or a tutor I hire on wyzant.com.
I was told a small magnet can be attached to the pole and used to represent a tangent vector. Would this be a flattened cylinder or a totally flat magnet?
I inserted a dotted line in the diagram. This is intended to represent a curved line in the surface of the ball. This would be printed on the ball, along with the legend.
I need proof that the magnet works before finalizing the printing. The magnetic pull from the metal ball on the magnet needs to be decreased so the magnet sticks out straight. I understand that there are limitations and the magnet can stay on only so firmly. Would I view a video of the printed ball with the magnet attached?
Three suggestions:
- Put holes in the ball directly where the magnet’s shadow would be. The curved line in the surface would then appear as a dotted line.
- Use a very short magnet and attach a plastic extension which would not experience any magnetic pull. This seems doable only if a flattened cylinder is used for the magnet.
- The base of the magnet is thicker than the rest of it so it is attached firmly while the extension is thin, experiencing little magnetic pull.
If the ball is printed soon, there will be a time gap before the next version is posted on mcneel.com. Given the job commitment where I work I’ll need time to verify the exact equations. At least having one ball in my hand will let me know the idea works.
Gary Willick
