|Finished Parabolic Template|
Then I put the point of my compass at the vertex of the right angle and drew a circle centered on it.
Satisfied that the distance was neither too large nor small, I used the compass as dividers to measure the same distance along the lines; as a check, once I was done, I opened up the compass and confirmed the ticks I'd put along the lines were on the same ever-increasing circles.
I numbered the ticks along the lines 1 through 8 so I wouldn't get confused.
Then I used a straight edge to connect points 1 to 8, 2, to 7, 3 to 6, etc. The result is an approximation of a parabolic curve. If I'd used more points and spaced them closer together, I'd get a more accurate curve.
I cut out the cardboard to use as a template. I snipped off the origin by cutting a straight line through points 1 to save material.
We'll see if it actually gets used as a template. The idea was to trace the shape on stiff construction paper, slot eight cutouts together, then fit aluminum foil over resulting paper frame; but the Mad Scientist got bored and went on to other Mad Science, so I may have to make the solar death ray generator myself.