Not more than fifteen years ago, “Pi Day” was a weird quirky day to “celebrate”. I’m heartened to see that March 14th, written as 3/14 in the dreaded Month-Day format has become a fun, light-hearted, and popular event to celebrate.
Pizza places and grocery stores have made it into a marketing event.
ShopRite, for example, calls it “National Pi Day” (it’s National!) and offers a free pie on their website.
Then you’ve got Blaze Pizza doing their thing with a $3.14 pizza pie for Pi Day.
So if on this day, you are getting pie and you’re worried about how to divide it fairly, let me introduce you to the “divider-chooser” algorithm.
Several years ago, I did a classroom visit as part of community outreach work that I do to promote mathematics in the classroom. It was a second grade classroom and our topic was about “fair sharing”.
So you’ve got a pie and want to divide it in half. Who divides it? If you divide it and pick the half, you’re incentivized to optimize for yourself. If the pie is yummy, you’ll give yourself “the bigger half”. But, if one person divides and the *other* person chooses, now, the divider is “controlled” enough to make sure that the cut is equitable. Equitable does not have to mean 50-50, though that’s often what happens.
What’s nice about divider-chooser is that the shape of the object doesn’t have to be symmetrical (think chocolate chip cookies that perhaps might not have had chocolate chips evenly distributed).
The theory of divider-chooser is rich and is part of the larger theory of incentives found in game theory. There are similar methods for how to fairly divide resources (think: budget, physical resources, arguing kindergarteners, etc.) among many individuals who have equal say in divvying up said resources. If you’re curious reach out.
To my educators and parents, you can read more about “Fair Sharing” in this four part series.
http://mathmisery.com/wp/2017/03/04/fair-sharing-for-second-grade-part-1/
http://mathmisery.com/wp/2017/03/05/fair-sharing-for-second-grade-part-2/
http://mathmisery.com/wp/2017/03/06/fair-sharing-for-second-grade-part-3/
http://mathmisery.com/wp/2017/03/07/fair-sharing-for-second-grade-final-part-4/