Yesterday as I was picking up my kid from a sleepover, I asked (knowing the answer would be pizza), “What did you have for dinner last night?”  Here is how the conversation went from there…

Kid:  When we got there, B said, “Here’s three pieces of pizza for you.” He had already eaten six.

Me:  That’s impossible.  Pizzas don’t get cut into nine slices.

Kid:  This was a square pizza.

Me:  OH!  That’s so cool!  Of course it was cut into nine pieces!  A square!  Get it?

Kid:  MOM.  Do you have to see math in everything?  Garumph.

Me:  I don’t have to see math in everything.  I just do.  I can’t help it.

 

Fast forward to right now.  The whole house is quiet but I am up because there is what feels like copious daylight and the birds are singing.  It’s the First Day of Spring!  Or as I like to exclaim, Happy Vernal Equinox!  Today everywhere on Earth, no matter which hemisphere, no matter which latitude, has the same amount of daylight.  Everyone from Oxford Mississippi to Sao Paulo, Brazil, to Sydney Australia, to the South Pole will experience roughly 12 hours of daylight today.  Then, locations in the northern hemisphere will continue to gain daylight (though at a decreasing rate) until the Summer Solstice (or the First Day of Summer) while southern hemisphere locations (Happy Fall Y’all) will be losing daylight (also at a decreasing rate) until June 20th (their Winter Solstice, or First Day of Winter).

A fun thing to do is to have your students calculate and then chart the amount of daylight for an entire year for their home town and for another more extreme (or less extreme as the case may be) location.  You can find great data at this  Navy site ; do just 12 calculations at one month intervals — and I am old school… I would want them to calculate and plot paper and pencil first before they go to a cool graphing software like desmos.  When I taught precal/trig, or algebra 2, I always had the students do this as an activity before we graphed sinusoids, because guess what?  We live on a sinusoid called Daylight.  So much fun!  The students also were blown away when they looked up the data (in the old days I had to print out a table for them) because we know precisely when the sun will “rise” on any given day at any given location for hundreds of years.  It’s a periodic function… period roughly 12 months, vertical translation roughly 12 hours, amplitude… well that depends on your location, and phase shift a little to the left.  If you live in the southern hemisphere your daylight graph will resemble

y = cosx,

and if you live in the northern hemisphere your daylight graph will resemble

y = -cosx.

 

Here I am at (approximately) the point (3, 12):

 

Come to think of it, my students did not just do a couple of graphs on this but an entire project on it too.  I will have to dig up that project and post it online for everyone to share. But for now, folks in my house are waking up and it’s time to cook the bacon…

UPDATE:  You can download the entire project for free by clicking here.