If you want to learn more about hyperbolas, you can construct the hyperbolic slot without using the prepared template. Hold a manila folder perpendicular to the base, along the centerline of the base between the dowel and the far end of the base. Plot the hyperbolic curve by making marks where the ends of the rotating arm cross the plane of the manila folder, and where the midpoint crosses the plane. Bend a piece of flexible material so that it crosses each of the three points and makes a smooth curve. Cut out this curve from the manila folder. Place the folder between the blocks on the base (shim it with crushed paper or some other improvised material to hold it upright and steady if necessary), and rotate the arm slowly through the slot. Make additional cuts where necessary to allow the wooden arm to move smoothly through the slot without touching. Then either use the manila folder itself for the slot (if it is stiff enough) or transfer the slot pattern to foam board or clear plastic and cut it out with an appropriate tool.
Change the angle of the dowel to vertical and visualize the shape of a slot that would allow the dowel to pass through it. Then position the dowel horizontally and visualize the shape of the slot it would need now.
Being able to visualize how the rod goes through the curved slot may help you the next time you have to move a long sofa through a doorway, along a hallway that turns a corner, or up a spiral staircase.
Did You Know?
A hyperbola can be described by a specific mathematical equation:
Y = 1 / x