Did you know that the ratio of the circumference (the distance all the way around) to the diameter (the distance across) of a circle is always equal to the same number? The number begins 3.14159, and no matter how many decimal places you take it to, it never ends! This crazy (well, mathematicians would call it irrational) number is called pi. Its symbol looks like this: π

March 14 (or 3/14) is Pi Day! In honor of this international celebration, we've put together some math activities for you to enjoy. For more formal math lessons, check out our Mensa For Kids lesson plans on shapes, probability, fractions, and Fibonacci numbers.

**Pi Day Palooza Activity Bundle**

Our Pi Day Palooza activity bundle of five no-prep, hassle-free pi-themed activities, along with a bonus coloring sheet, is included in this extension. Flip to the end to find it!

**Calculate Pi**

Calling all circular household items! Measure the diameter and circumference of cans, jars, glasses, bowls (even toilet bowls!), and rugs to see if you can find *π* in your house. To find *π*, divide the circumference of the circle (all the way around) by the diameter (the length from one side of the circle to the other):

Try using several different sized circles and see how close you get to 3.14!

**Pi Paper Chain **

Even the youngest mathematician can participate in this activity! Different colored paper strips are paired with numbers (e.g., blue for 2, red for 4). The strips are then linked in the order of π (3.1415…). The chain can be as long or as short as time and interest allow.

What you need:

- Construction paper of ten different colors cut into strips
- Stapler, tape, or glue

What you do:

- Decide which color will represent which number.
- Create your paper chain by taking a strip of paper in the color you have chosen to represent the number 3 and making it into a loop. Close the loop with a stapler or piece of tape.
- Take a strip that represents the number 1 and thread it through your loop. Close the loop.
- Repeat with the strips that match the numbers in πso that you have a visual representation of π.

**How long can you make it? Here are the first 500 decimal places to get you started:**

3.1415926535897932384626433832795028841971693993751058209749445923078164

062862089986280348253421170679821480865132823066470938446095505822317253

594081284811174502841027019385211055596446229489549303819644288109756659

334461284756482337867831652712019091456485669234603486104543266482133936

072602491412737245870066063155881748815209209628292540917153643678925903

600113305305488204665213841469519415116094330572703657595919530921861173

819326117931051185480744623799627495673518857527248912279381830119491

**A Homemade Spirograph**

All it takes is a few minutes with a Spirograph to remind you how fun drawing a plain circle can be!

What you need:

- A round cake pan (or other flat, round pan)
- Cardboard
- Scissors
- A rubber band
- A pencil
- Paper
- Tape

What you do:

- Measure the diameter of the cake pan.
- Draw a circle with a diameter half that of the pan. You can do this easily by making one side of the square you use to draw the circle (as described in the activity above) the length you want for the diameter.
- Trace it on the piece of cardboard.
- Put the rubber band around the edge of the piece of cardboard.
- Cut out a piece of paper to fit the bottom of the pan and use tape to hold the paper in place so it doesn't move around.
- Poke a hole in the middle of the cardboard. If you don't want to make circles, you can get weird shapes by making the hole away from the center of the circle.
- Put the pencil in the hole and move the circle around the cake pan. Hold the edge of the pan with one hand so the pan doesn't move while you're moving the circle. The circle will guide the pencil to make cool shapes on the paper in the bottom of the pan. Try it with different color fine-tip markers. The circles you're drawing are called hypotrochoids. Cool name, huh?

Use Martin Gardner's Spirograph to see that same idea on the computer.

(We need to give credit for this idea to Martin Gardner, a mathematician who wrote about cool things to do with math in *Scientific American*).

**Pilish Poetry**

Pilish is a form of writing based on pi. When writing in Pilish, the number of letters in each word used correspond to the digits in pi, meaning the first word will have 3 letters, the second 1 letter, the third 4 letters, until you’ve reached a stopping point. For an example:

*Was I just a happy jellyfish, so bouncy, light, and small, drifting clockwise however aimlessly, sea to sea, evermore. *

There are a few forms of Pilish – **Basic Pilish**, which treats every 0 digit in pi as a 10 letter word, and no words greater than 10 letters are used, and **Standard Pilish**, which allows writers the freedom to combine smaller consecutive numbers (like 1 and 2) into a single 2 digit number (like 12) so words with more than 10 letters can be incorporated. Pilish can also be **Alphabetic**, which uses only letters and ignores numbers, or **Alphanumeric**, which counts numbers as letters as well.

Pilish can be used as a mnemonic device to help memorize the digits of pi. Try writing your own poem or story in Pilish – see how many digits you can get to! Use this online Pilish Checker to make sure you haven’t miscounted your letters. *Note: this tool uses Alphanumeric Standard Pilish, so if you’ve written your poem using Basic and/or Alphabetic Pilish, it may not work.*

**Pi Art**

Channel your inner artist and create something beautiful for Pi Day. There are lots of ways to incorporate art into your Pi Day celebrations. Here are some examples:

__Pi Tape Resist Art__

What you need:

- Watercolor paper (or other white paper)
- Watercolor paint
- Paintbrushes or sponges
- Painter’s tape
- Dish of water

What you do:

- Use painter’s tape to make a π symbol on your paper. Press down on the tape to make sure there are no gaps where your paint can get through. You want your pi symbol to remain white.
- Use your water to wet your brush, then begin painting around your tape. Add as many colors as you like – you can do a simple border around your pi symbol, shapes, designs, or color the whole page!
- Wait at least 30 minutes for your paint to dry.
- When your paint is dry, carefully remove your tape.

__Pi Calligram__

A calligram is a type of artistic poetry that mixes words with visual art – artists create an image made entirely out of words that describe, relate to, or in some way represent the subject of the image.

What you need:

- Paper
- Pencil
- Pen or fine tip marker
- Eraser
- Digits of pi (optional)
- Pi vocabulary list (optional)

What you do:

- Decide what shape you’d like your calligram to be. We recommend a circle or pi symbol. Then decide whether you’d like to use the digits of pi to create your calligram or words that are associated with pi.
- Sketch an outline of your shape on your paper using a pencil.
- Using your pen or marker, write your words or numbers along your outline.
- When you’ve completed your picture, erase your pencil outline.

__Pi in the Sky__

Turn a bar graph made of pi’s digits into a city skyline.

What you need:

- Graph paper
- Black pen or fine tip marker
- Colored pencils, pens, or markers
- Digits of pi

What you do:

- Using your black pen, fill in 3 blocks along the y axis (depending on the size of the blocks, you may want to double or triple the number of blocks used for each paper. Whatever you decide, make sure you use the same multiplier for each digit). This will make your first building and your first digit of pi.
- In the next spot along the x axis, fill in 1 block for the next digit of pi, then 4 blocks vertically in the next spot along the x axis, and so on, until you’ve made as many buildings as you like. For 0s, use 10 blocks.
- Once your pi digits have been graphed, add details to your background. Get creative!

**Pi Around the Web**

Looking for more Pi Day fun? Check out these websites:

Pi Day at the Exploratorium - Pi Day history and activities, courtesy of the museum where Pi Day began

The NASA Pi Day Challenge – Solve problems using pi just like a NASA scientist

Your Pi Birthday – Calculate your age in pi years

Pi Day Facts – 25 fun facts about pi and Pi Day

The Pi Game – See how many digits of pi you know!

Mensa for Kids Activity Plans are designed to simultaneously entertain and challenge gifted youth in their time outside of the school setting; however, the activities may be easily shared and enjoyed by older people as well. Programs may be scaled up or down depending on number of attendees, desired level of complexity, etc. Sample materials are included with most plans. This activity plan was developed by Lisa Van Gemert, M.Ed.T., the Mensa Foundation’s former Gifted Children Specialist. If you have questions or comments about these programs, please email our Gifted Youth Programs Manager.