Birthdays

As a kid, I always liked the fact that my birthday was during the summer.  That way, I didn’t have to be the centre of a party in class and all that goes with it.  I’m not the type of person that enjoys that sort of thing.

Now, it’s kind of cool that social media knows my birthday and takes the opportunity to say “Happy Birthday”, and I appreciate that.

My quote of the year comes from my friend Tammy who had a T-Shirt with this on it.

2017-08-14_0932

If you don’t get it, have a gamer explain it to you.

Anyway, the concepts of birthdays gets really interesting when you turn to birthdays and mathematics.  There’s a very famous problem; the “Birthday Problem“.  It’s pretty heady stuff involving probability and so generally doesn’t appear in mathematics until a good background has been established.

But, it’s one of those things that let you discuss mathematics without necessarily writing a proof for the problem.  It boils down to the probability or chance that two or more people in a group will have the same birthday.

It’s also the stuff that Computer Science teachers love to give out as a problem.  You can work up to it.  For example, give a program your birthday and have it determine what day of the week you were born on (don’t forget leap years).  If you’re not up to writing the code, check this out.  Even if students aren’t ready to write the code, it’s the sort of activity that inspires thinking about how a computer might be programmed to solve the problem.

Back to the Birthday Problem.  It’s something that’s quite surprising in real life.  In our department of about 30, there were three of us who had the same date for a birthday (that I knew about).  It’s still surprising when you consider that there are 365 days in a year.  Surely, there’s enough elbow room there that there would be no duplicates!   It’s a reality for teachers.  In any class, there always seems to be students who share the same birthday.  Even more interesting, because of sample size, they share the same birth year!  Stepping back, you see it again if you’re trying to ride herd on a homeroom during morning announcements which always seem to include a long list of Happy Birthday wishes.  In a school with 1,200 students, it only seems reasonable that there might be three.  That never seemed to work out!

The mathematics behind the Birthday Problem is interesting.  You can read the details here.  Or even here.  I can recall having one of those off-the-cuff discussions with a student about it and he thought that he’d write a program to simulate it.  Neil, if you’re reading this, did you ever finish it?

If not, here are a couple of online efforts …

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