Today marks the Autumnal Equinox in the Northern Hemisphere. (It was at 3:02 PM Central Time.) In Mississippi it is impossible to enumerate the number of painted “Happy Fall Y’all” signs festooning doors not to mention the number of mums and pumpkins cascading down front steps. And yet, we are experiencing temps in the low 90s. We don’t really have Fall, y’all, trust me, I know what Fall is. In Mississippi we have Summer and then Winter. By late October the weather will switch from being stifling to cold and I will switch from wearing flip flops to cowboy boots.
But we do have Fall on the calendar in Mississippi (it begins today), and we have been experiencing a rapid loss of daylight these past few days. It is always dark when I get up for school at 5:17 am, but the past few mornings I have seen and heard some critters that usually lurk in the shadows. The other day it was a rat on my early morning dog walk and this morning it was a loud owl. So, the animals know that the night is lengthening, even if the temperature isn’t cooling off.
The past few days my calculus students have been sketching derivative graphs given unnamed graphs of parent functions (y = x^2, y = x^3, y = lnx, y = 1/x, y = sqrt(x), y = e^x, y = sinx, e.g.) by just estimating slopes and plotting those y’ values versus the x-values (very low tech pencil and paper stuff). They were starting to notice that lots of them have recognizable derivatives. So this morning’s warm up was for them to sketch the derivative of this graph:
Of course the math folks reading this will recognize it as y=cosx and immediately say that the derivative is -sinx. But not so with the students. They (mostly) carefully made a table of values and plotted their points before coming to a conclusion. After we went over their results, some were curious about what the derivative of -sinx would be. The fun didn’t stop there. They decided to carry the pattern through and realized these periodic functions have a pattern in their derivatives.
So then I explained where we are on the daylight graph and why today is such an important day. Today it’s not that y’ =0, but that y” = 0. We are on the part of the daylight graph where we are losing daylight at the most rapid rate. The rate is a maximum of sorts.
Here is what our daylight graph looks like for one year in the Northern Hemisphere (locales’ amplitudes will vary based on latitude):
On this graph we are at about (280, 12) today.
So, Happy Fall, Y’all and keep posting those apple picking pictures my Northern friends!
Other blog posts on the change of seasons that you might enjoy: