Irrational and Transcendental Number Fun for Pi Day: Pi Dice Game

In case you have been living under a rock, we love dice games! And of course because my eldest son was born with with an obsession for numbers we love to celebrate Pi Day (March 14th), as we did once by creating these gorgeous pi city skylines. This year I thought, hmmm, how can we turn pi (π) into a pi dice game?

I noticed that Math Geek Mama invented a cool pi themed card game, so I figured we would turn our thoughts towards a pi dice game that would help kids memorize the numbers in pi.

First, what is π?

π is the ratio of the circumference of a circle to its diameter; the numbers in π never repeat and contain no patterns.  It is also an irrational number, meaning it is a real number that cannot be written as a simple fraction.

Pi is a transcendental number, too, which sounds like it enjoys meditating in a lotus garden but really it means it "is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients."*  Meditating in a lotus garden sounds pretty good right about now, doesn't it?

π begins 3.14159..., but mathematicians have so far calculated it  to more than a trillion digits!

The pi dice game is super simple, and hey! you can adapt it to any string of numbers you want. (Note: this post contains affiliate links)

What you need:

• 2  dice; it's waaaay more fun when everyone has their own colored dice!
• This printout of the number π
• Pen and paper to keep track of your rolls
• 2 or more players who love the number π!

Objective: 

Roll the largest string of pi digits.

How to play:

Taking turns players roll both dice. The object is to roll out the digits of pi. On the first roll, each player is aiming for a 3. This can be a roll of 3 on one die, or the combination 1-2. If the player is successful, he records his number and takes another turn, aiming to roll the next number in pi. If he does not roll the correct number, his turn ends and game play passes in a clockwise direction.

If a player rolls two numbers in the pi sequence, he can record them both. Each die can only be used for one number, so a roll of 5-4 could count as a 5 and a 4, or a 9, but not a 5 and a 9 (5+4).

For example:

Player 1: rolls a 1-2, records "3"

Player 1 rolls again: rolls 3-4. Turn ends.

Player 2: rolls 3-1, records "3.1"

Player 2 rolls again: rolls 2-2, adds a 4 to his record, which now reads "3.14"

How long does the game last?

Determine ahead of time how long you wish to play. Play can be limited by time–for example, whoever has the most pi digits after 10 minutes is the winner. Or, the quantity of numbers can be set–for example, whoever reaches the 25th digit of pi first is the winner.

Note: this pi dice game does not teach children the mathematical concept of π, but it is a fun way to while away the time on Pi Day and it will give kids a hands on feel for the enormity of the number itself!

Don't forget to check out more number fun: 

• Pi Day art projects for kids
• Fibonacci art project
• Lu-lu math dice game from Hawai'i

And of course, our pi skyline activity!

*It's true, I got that definition from the Wikipedia page.