A hyperbolic paraboloid (on the right) is a beautiful curve that has hyperbolic cross-sections horizontally and parabolic cross-sections vertically. Yet the strings that make up this shape all form straight lines.

If you use the same base, but thread the string differently, you can create a model of Plücker's conoid, another ruled surface.

- A cylindrical cardboard container about 3¾ in. (9.5 cm.) in diameter. This seems to be a standard size for food packaging in the U.S. The above model was made from one Ovaltine container. You can scale the print of the PDF file if your cylinder is a different size than this.
- Embroidery thread.
- Craft knife.

- Tape the patterns together and then onto the cardboard cylinder.
- Cut the cylinder in half along the sine wave with a craft knife.
- Make small slits in the cardboard at each mark. Remove the pattern from the cardboard cylinder.
- Tape the end of the thread to the cardboard container near the lowest slit on the curve.
- Stretch the thread from the slit in the valley to the one on the top of the hill.
- Slip the thread into the next slit farther away from the first slit and stretch the thread across the container. The string should make a checkerboard pattern when viewed from above.
- Continue until you reach the next mountain-valley pair.
- Use a different color thread and repeat, this time connecting different mountain-valley pairs.
- To make the conoid stretch the string from one slit to the slit directly opposite it. From above, the strings forming the conoid look like spokes of a wheel.

- Fischer describes the formulas governing these shapes. Construct a curve on cylinder . With string create line segments PQ and PQ' where , , and to create a hyperbolic paraboloid with the equation .

Connect points P with P' where and to get Plücker's conoid with the equation

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