Then I thought to myself, what if I enlarged the picture, could the picture be more useful? Saving the picture to storage was the first task. Then we loaded the picture into a viewing program. There you could enlarge the picture and save it in the expanded format.

So far so good. Then I printed out the picture. Still do not have a parabola yet. Then it was time to get out the scissors and cut between the splines. Easy enough. Now just one last step in that we need to attach the splines together. Cellophane tape makes that easy.

If you add foil before you cut the parabola up, can make things interesting.

Then I thought, what about an even larger parabola. Poster size maybe. Extend out the spline edges with a straight edge (not like the crude extensions in the picture).

The we could make an even larger parabola all based on the original tiny picture. Let you do that yourself. Let's see solar cooker, sound umbrella, hat, or etc etc.

Update: Found another parabola to print out. The original was all black and emptied the ink cartridge. Went into gimp and reversed the colors.

Time for an even larger one!

x y

0 0.0000

3 0.1875

6 0.7500

9 1.6875

12 3.0000

15 4.6875

18 6.7500

21 9.1875

24 12.0000

27 15.1875

30 18.7500

33 22.6875

36 27.0000

39 31.6875

42 36.7500

45 42.1875

48 48.0000

The formula for a parabola is:

y = x² ÷ (4 × p)

where p is the distance from the bottom of the parabola to the focal point, and x and y are cartesian coordinates of points along the parabola.

For a parabola that is to be 96 inches across (that is, -48 inches to +48 inches relative to the focal point) and 48 inches deep, with a focal point 12 inches above the bottom of the parabola, the formula generates the numbers shown in the table on the right.

Sometimes it is useful to be able to locate the focal point after the fact. Rearranging the above formula

p = x² ÷ (4 × y)

where x is the width (from the focal point) of the parabola, y is the depth of the parabola, and f is the distance ahead of the bottom of the parabola of the focal point. For our above 96 inch wide and 48 inch deep parabola, f solves to 12 inches.

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