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Pi Day March 14, 2011

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Today is Pi Day, 3/14!  Here are some Pi Day activities courtesy of Lisa Van Gemert at the Mensa Foundation.

Pi Day Fun

Did you know that if you take the ratio of the circumference (the distance
all the way around) to the diameter (the distance across) of a circle, it
will always equal the same number?  The number begins 3.1415, and it never
ends!  This number is called Pi.  It is written like this: π 
Did you know that March 14 is Pi Day?  In honor of this day, we’ve put
together 3.14 math activities for you to enjoy.

3 Math Lessons
These lessons can be downloaded by logging on to www.mensaforkids.org.
*    Shapes (Kindergarten)
*    Action Fractions (2nd Grade)
*    Probably Probability (6th Grade)

14 Pi Day Activities
Here are 14 Pi Day Activities that you can do for fun and learning at home
or at school.

1.    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 or tape

What you do:
*    Decide which color will represent which number.
*    Create your paper chain by taking a strip of paper 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 Pi so that you
have a visual representation of Pi.  How long can you make it?
*    Here are the first one million digits to get you started:
3.1415926535 8979323846 2643383279 5028841971 6939937510
  5820974944 5923078164 0628620899 8628034825 3421170679
  8214808651 3282306647 0938446095 5058223172 5359408128
  4811174502 8410270193 8521105559 6446229489 5493038196
  4428810975 6659334461 2847564823 3786783165 2712019091
  4564856692 3460348610 4543266482 1339360726 0249141273
  7245870066 0631558817 4881520920 9628292540 9171536436
  7892590360 0113305305 4882046652 1384146951 9415116094
  3305727036 5759591953 0921861173 8193261179 3105118548
  0744623799 6274956735 1885752724 8912279381 8301194912

2.    Pi for Foodies!
Since π is all about circles, foods like cookies or pancakes make great Pi
Day foods.  Here are recipes for Pi Day Cupcakes and our secret Mensa
frosting recipe, along with other Pi Day food ideas!

Easy Pi Day Cupcakes
Ingredients:
2 1/4 cups flour
1 1/3 cups sugar
3 tsp. baking powder
1/2 tsp. salt
1/2 cup shortening
1 cup milk (use whole milk for a moister cupcake)
1 tsp. vanilla
2 eggs (large)

Directions:
1.    Preheat your oven to 350º. 
2.    Grease muffin tin or line with cupcake liners.
3.    Mix all dry ingredients (flour through salt) in a large bowl.
4.    Add the shortening, milk and vanilla.  Beat well for one minute at
medium speed.
5.    Add the eggs and beat for one more minute.  Get the batter off the
sides and mix at high speed for 1 ½ minutes.
6.    Use an ice cream scoop to put the batter into the muffin tins,
filling about 1/2 to 2/3 full. 
7.    Bake for 20-25 minutes until the tops bounce back when you touch
them or a toothpick comes out clean.  Cool completely before frosting.

Secret Mensa Frosting Recipe (makes enough to frost two dozen cupcakes)
1 lb. powdered sugar
1/2 cup shortening (we used Crisco®)
1/4 cup water
1/2 tsp. each butter, vanilla, and almond flavoring
pinch of salt

Tint as desired with food coloring (paste works best).  Mix well and
spread! 

Other Pi Day food ideas:
*    Make the Pi symbol (π) out of pretzels, hot dogs, mini-carrots, or
any other long, straight food.
*    Make pie, of course! 
*    Make circle cookies or pizza and use them to calculate pi!

3.    Pi Bracelets
Inexpensive plastic beads twisted onto pipe cleaners or jewelry-making
chains from the craft store can be used to create mathematical bling! 

What you need:
*    plastic beads
*    pipe cleaners, yarn, or other product on which to string the beads

Like the paper chain, you will choose a color of bead to represent each
number from 0 – 9.  Thread the corresponding bead in the order of pi to
make a bracelet (on pipe cleaner) or a necklace (using yarn, etc.).  Voila!
Wearable math bling!

4.    Pi Day Couture
All you need is a solid-color t-shirt, a bottle of bleach, and our template
to rock this cool Pi Day look!
What you need:
*    Colored t-shirt (darker colors work best)
*    Stencil (included here)
*    Spray bottle with 50/50 bleach and water solution in it
*    Foil, cardboard, or newspaper

What you do:
*    Lay the shirt on a flat surface that you cover with foil,
cardboard, or newspaper to protect it from accidental bleach spray.  You
may wish to put a piece of foil between the front and back of the shirt to
prevent the bleach from bleeding through, but this is usually not a problem.
*    Cut out the stencil and lay it on the shirt.  If you have a big
shirt, cut out several stencils and lay them out in a pattern on the shirt.
*    Using the spray bottle, spray the bleach/water mixture on the shirt
and watch as the shirt changes color.  Repeat until the shirt is the color
you want.  Make sure it is light enough around the edge of the stencil that
the stencil will show up!
*    Remove the stencil.  Wash the shirt separately with very little
detergent for the first wash.

5.    The Never-Ending Number Story
Pi Day isn’t just for math junkies!  Readers and writers have a role as
well.  Here are some things budding writers and savvy readers can do to
celebrate this amazing number.
*    Write a poem in which each line corresponds to the number of
syllables in pi.  So, you would have three syllables in the first line, one
in the second, four in the third, one in the fourth, and so on.  How many
lines can you write?
*    A more intense writing activity is to create a myth melding π and
the ancient Greeks.  Can you come up with a story about how the ancient
gods created, used, or abused pi?
*    Analyze Wislawa Szymborska’s poem Pi (below).  You can use the TP-
CASTT method to analyze it (see below the poem).
Pi by Wislawa Szymborska

The admirable number pi:
three point one four one.
All the following digits are also just a start,
five nine two because it never ends.
It can’t be grasped, six five three five, at a glance,
eight nine, by calculation,
seven nine, through imagination,
or even three two three eight in jest, or by comparison
four six to anything
two six four three in the world.
The longest snake on earth ends at thirty-odd feet.
Same goes for fairy tale snakes, though they make it a little longer.
The caravan of digits that is pi
does not stop at the edge of the page,
but runs off the table and into the air,
over the wall, a leaf, a bird’s nest, the clouds, straight into the sky,
through all the bloatedness and bottomlessness.
Oh how short, all but mouse-like is the comet’s tail!
How frail is a ray of starlight, bending in any old space!
Meanwhile two three fifteen three hundred nineteen
my phone number your shirt size
the year nineteen hundred and seventy-three sixth floor
number of inhabitants sixty-five cents
hip measurement two fingers a charade and a code,
in which we find how blithe the trostle sings!
and please remain calm,
and heaven and earth shall pass away,
but not pi, that won’t happen,
it still has an okay five,
and quite a fine eight,
and all but final seven,
prodding and prodding a plodding eternity
to last.

    TP-CASTT
Step 1: Analyze the title. It’s easy for this poem, isn’t it?
Step 2: Paraphrase the poem. That means to put it into your own words. You
can do this line by line or word by word. Use a thesaurus to find strong,
evocative synonyms.
Step 3: Connotation means what the words and phrases convey that they
don’t say explicitly. Look to the metaphors the poet uses. To what does he
compare pi? What other figurative language can you find?
Step 4: What do you think the poet’s attitude is?
Step 5: Can you find any shifts in the poem? Look for when the subject,
attitude, mood, or motif.
Step 6: Go back to the title again. What do you think the poet feels about
the subject of the poem?

    6.    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 are able to 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).  Do you get close?

7.    Circle Drawing Contest
All it takes is a few minutes with Spirograph to remind you how fun drawing
a plain circle can be!  Being able to draw a good circle (one that isn’t
flat or elongated) is a great skill, and it’s easier than you may think.
Here’s how:
You start with a square.  Sounds weird, doesn’t it?
How to do it:
1.    Draw a square.  It’s easier to draw a good square than a circle,
which is why this helps!
2.    Next, draw a second square on its edge inside the first square.
3.    Now draw an “x” from across the square really lightly with your
pencil.
4.      The last step is to draw the circle.  Using your pencil, lightly
draw in short arcs from one reference point to another.  The squares and
the X give you shorter lengths to go, so you can keep your circle balanced
quite easily.  Once you are done, erase the squares and the X and fill in
any gaps in your circle.

See who can draw the best circle.  How big can you make a really good
circle?
You can do something really cool with a good circle!  Here’s how to make a
homemade Spirograph.

What you will need:
*    a round cake pan (or other flat, round pan)
*    cardboard
*    scissors
*    a rubber band
*    a pencil
*    paper
*    tape

How to do it:
1.    Measure the diameter of the cake pan.  Now draw a circle with a
diameter ½ that of the pan.  You can do this easily by making the a 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. 
2.    Put the rubber band around the edge of the piece of cardboard
3.    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.
4.    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.
5.    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?
P.S. If you want to try this same idea on the computer, the website below
lets you try it:
http://wordsmith.org/~anu/java/spirograph.html

(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). 

8.    Pi trivia
Go to this site to calculate your age in pi years: http://pidays.jtey.com

9.    Surrounded by Pi!
Read about in these books:
A History of Pi
The Joy of Pi
Sir Cumference and the Dragon of Pi
Life of Pi
Contact
Pi: A Biography of the World’s Most Mysterious Number
Not A Wake: A dream embodying (pi)’s digits fully for 10000 decimals

Watch movies about π:
Pi (1998 thriller)
The Net (1995)
Torn Curtain
See clips of math in movies at:
http://www.math.harvard.edu/~knill/mathmovies/
See short movies to learn about pi at:
http://www.projectmathematics.com/storypi.htm
Watch a short video to learn more about pi at:
http://video.google.com/googleplayer.swf?docid=-6200593424291031420&hl=en&fs=true

10.    Singing Pi
Celebrate Pi Day with a special song!  Sing the song below to the tune of
“O, Christmas Tree.”

Oh Number Pi written by LaVern Christianson
Oh, number Pi
Oh, number Pi
Your digits are unending,
Oh, number Pi
Oh, number Pi
No pattern are you sending.
You’re three point one four one five nine,
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.
Oh, number Pi
Oh, number Pi
You are a number very sweet,
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There’s 2 Pi r and Pi r squared,
A half a circle and you’re there,
Oh, number Pi
Oh, number Pi
We know that Pi’s a tasty treat.

Can you write one yourself?  Listen to Pi by Kate Bush to get an idea!

11.    Cutting Pi
See if you can try this “magic” trick on a friend.
What you need:
*    something circular
*    string or yarn
*    scissors
What you do:
1.    Wrap the string or yarn around the outside of the circular object
(the circumference). 
2.    Cut the string to the exact length of the circumference.
3.    Take the cut piece and lay it across the diameter of the circular
object.  Cut the string that length.  Repeat. How many pieces can you cut?
4.    No matter how big your circle is, you will always be able to cut
three pieces with a little bit more left over.  You have cut pi!

12.    Making Pi a law!
Find out about the state legislature that tried to decide for good what pi
was really equal to!
In 1897, a representative in Indiana introduced a bill to make π a normal
number like any other instead of the beautiful irrationality it really has.
He proposed three numbers that people could use for π in different
situations.  Here are his suggestions:
(1) The ratio of the diameter of a circle to its circumference is 5/4 to
4.  This made π equal 16/5 (3.2).
(2) The area of a circle equals the area of a square whose side is 1/4 the
circumference of the circle. This made it 4.
(3) The ratio of the length of a 90 degree arc to the length of a segment
connecting the arc’s two endpoints is 8 to 7. This made pi equal to the
square root of 2 x 16/7 about 3.23).
It was actually even more complicated than this, but it was passed by the
House of Representatives.  In the Indiana senate, the bill would have
passed except that there happened to be a mathematician who read it and had
a heart attack right there on the spot.  Well, not a real heart attack, but
he was surprised to say the least. 
The bill died there and was never heard from again.  Pi was the winner and
still irrational champion!
13.    Pi day greeting cards
Create cards to send to friends and family celebrating Pi Day (or
Einstein’s Birthday – one in the same!).

You may use any of the following ideas for things to write on the cards, or
come up with some of your own:
*    Happy (insert a picture of piece of pie)Day !
*    You are sweeter than
3.14159265358979323846264338327950288419716939937510
*    When the moon hits your eye like a big pizza π that’s 3.1415…
*    Circles…they’re as easy as 3.1415926535897932384626
You can also decorate with pi by downloading the pi poster at
http://unihedron.com/projects/pi/downloads/pi.pdf

14.    Making Music out of Pi!
Turn the numbers into a tune at this site:
http://www.avoision.com/experiments/pi10k/index.php

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