Turns out you can use CorelDraw to  reverse engineer the parts to a conic section model.  Read all about it in the November 2021 MAA Math Horizons page called Do The Math (p. 29).
Editor Tom Edgar was fun to work with, and made the graphic images.

Note:  if you are “making” this model from scratch, once you find the long and short axes of the ellipse, you could use the “trammel method” to find all its points. Here’s a youtube on that by TechSquare

The files are here, please help yourself.  We cut ours out of 1/8″ wood so the slots are that size – you may  need to adjust.

If you are in the US or Canada and would like a wooden model like this one we can send you one for free.    Please fill out this form and we will get back to you.  (note: EU countries are adding a 20 Euro tax on even one model so we cannot ship at this time- except in Spain where we have a partner.  Until we can add others, outside Spain  please download files to make locally.)

If you are a district leader, or conference organizer in the US or Canada, who could distribute a dozen or more to teachers, library, etc, please request a bulk shipment using this form.

8.5×11 Printable PDF of original design (glue to cardstock instead of wood and cut out)

The exterior of the cone for the original design is a semi circle.  You can make two quarter circles on 8.5×11 inch paper with radius equal to the side length of the triangle, tape them together and have a cone that fits.

SVG

Adobe Illustrator

Corel Draw

PDF

Files for 3d Printing Here
(Boardmember Alex’s friend Colin made these files and we printed them on Craftcloud-picture at bottom of post)

Make Conic Section Model Earrings with your 3d Printer and this STL file.  They look great!  The STL adaptation is by Ella Basken.

 

To make from “scratch”:

Start with an isosceles triangle and then draw lines – across for circle, parallel to a side for the midline of the parabola, across at angle for ellipse and vertical (or not parallel to a side) for the hyperbola.
Next use those lines to find the dimensions of the conic section pieces – diameter of the circle, the long and short axis for ellipse (use the chord at the base located a distance equal to the distance of the center of the ellipse to the midline of the triangle, parabola height (length of line) and width which is the chord where it intersects the base circle, and similarly for the hyperbola.)

Using this sequence we made  a pointier version as well in PDF 8.5 x 11

The “wrap” for the pointy version is made from a portion of the circle with radius equal to the side length of the triangle.  What part or fraction of that circle?  Only as much as can contact with the bottom of the cone.

Here’s a template for this one.

You can also slice Playdoh or clay to get a great conic section model.  Sometimes those get squishy, but you can repeat and experiment with different cones.

See a video made by Paola Garcia explaining further here:

 

I made a few extras!

 

Here’s a Cricut and a foam version posted to twitter by  Mark Kaerscher

And a 3d Printed model by  MathHappens board member Alex Siegel:

Folks are making their own versions with all kinds of materials and adding the shell is a great idea!

7/11/22 In Spain mathematics professors are making their own with scroll saw and dremel:

This is one  of the prettiest conic section model photos I’ve seen.

 

Our partnership with MMACA has been so productive!  This posting on facebook is a great picture of the MMACA version and  another way to see how far these are spreading.

Here’s another great photo:

Love to see our model on the table at a conference to help and inspire teacher leaders in San Diego.

Almost one year later on Nov 6, 2022, appreciation for this model is still spreading.  This is the version we co-sponsored with MMACA.  Museum of Math in Spain.