Creating an oblique circular cylinder isn't as easy as it seems. At first you might think that you can make one by simply cutting off the ends of a tube at a slant. However, this produces a cylinder with ellipses as bases, not circles. Creating the net of an oblique circular cylinder took some heavy mathematics.

- Cut out the pattern from card stock. Cut out two copies of the circle.
- Glue the strip into a cylinder.
- Fold the tabs down and glue the two circles onto the ends.

- The curvy sides of the net are not sine waves. They are a more complicated curve that requires elliptic integrals to calculate.
- To calculate the shape of the curve in this net, place a unit circle on the x-y plane and rotate it α degrees about the x-axis. Extend the cylinder up the z-axis. In this position, a horizontal cross-section of the cylinder is an ellipse with semimajor and semiminor axes of a= 1 and b = cos(α). This ellipse can be represented by the parametric equations .

The height of the circle above the x-y plane is the height of the curve at any point along the perimeter of the ellipse. The height of the circle is . The distance along the perimeter of the ellipse is given by the incomplete elliptic integral of the second kind .

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