Conic Sections Instruments Workshop
Viktor Blåsjö
v.n.e.blasjo@uu.nl


I have made 3D models of a number of historical instruments for drawing conic sections. These models can be 3D printed and used in a classroom or workshop setting. For this you need:

- The 3D printed models. More on this below.

- The workshop document with figures from historical treatises. This should be printed in the scale provided (my PDF is for A4 paper). In some cases (based on angles only) it would work at other printing scales too, but in a number of cases the printed sheet needs to align metrically with the scale of the 3D-printed instruments.

- 6 pushpins or thumb tacks of which at least 2 need to have a flat top. In the visual instructions in the workshop document you can see the thumb tacks needed. I make a distinction between the pushpin with a "handle" that provides the generating or "input" motion. You will be guiding this pushpin with your hand so the handle rather than a flat top is easier but either would work. For the other components I use flat-top thumb tacks in my illustrations. In many cases pushpins would work fine too, although occasionally the flat top is better since it enables other components to move over them if necessary. There are also some cases where a thumb tack is upside down. These are not attached to the ground but keep the components above them together. These thumb tacks need to be flat-top ones since they need to stand upside down flush against the working surface. Pushpins and thumb tacks of normal or standard size work well. Avoid those of smaller-than-standard size as they are too short.

- A surface receptive to pushpins. I use 5mm foam boards (A4 size). These are lightweight and work well.

The workshop consists in recreating the mechanisms shown in the historical figures. Take the workshop sheet with the figure and place it on the foam board. Place the corresponding 3D printed components on top of the figure as shown in the visual instructions. You should see the 3D components align with the figure underneath. After fastening the appropriate points, move the pushpin as indicated by arrows in the instructions. One of other the points of the configuration traces the conic section. I have marked this point with a pen icon, but this is to be regarded as an "imaginary pen": the goal is to see visually that the "pen point" traces the desired curve; it would be very impractical to try to fit an actual pen in there.

Besides the enjoyment of this hands-on experience, relevant mathematical questions to consider are for example to determine the asymptotes or limit points ("at infinity") of hyperbolas and parabolas, as well as focal points in the case of the van Schooten instruments.

3D PRINTING

I have provided STL files for 3D printing. You can print these using your own 3D printer, or order them printed from a 3D printing service.

For most purposes I recommend using the composite file that contains all instrument components in a single printing. This is less hassle to print and more convenient for packaging, transporting, and distributing to workshop participants. The composite file prints the instrument components and thin connectors that keep the pieces together in a single "sheet". This makes it easy to put together workshop packages by for example putting the workshop papers and the 3D-printed instrument sheet together in a plastic sleeve or folder for easy distribution and organization. When using the instruments, the thin connectors between the components are easily pulled off by hand.

I have also provided STL files for the individual components separately but these are redundant if you print the composite one.

SOURCE FILES

I made the 3D models using Tinkercad. I made the models public there:

https://www.tinkercad.com/users/1nGpVEfytUl

You need an account (free) to access these models. These models should be editable. From Tinkercad you can also export to other formats such as OBJ if needed.
