This is another post in my series on math in the real world.
When plants lean over due to being pulled by gravity, they often form a similar shape. With some exploration, we can determine what shape this is (at least approximately). First, I opened up one of these pictures and embedded it in Geogebra. Next, I added some points to my diagram, following along the shapes of one of the plants.
Next, I exported these points over to MS Excel, so I could find a regression on the points. A quick glance at the shape the curve seemed to be representing suggested I should try fitting the points to a parabola.
The shape does appear to be a parabola, however, I know from experience that not all parabolic shapes are what they appear. For example, a hanging line is actually a catenary.
What would you have to do to confirm that this shape is a parabola? Is it possible that it is only approximately a parabola?