Celebrating Math with Pi Day

Are your students doing anything special for Pi Day?

Back when we were homeschooling, my kids and I always felt stir-crazy after two months with no significant break. We needed a day off — and what better way could we spend it than to play math all afternoon?

I love any excuse to celebrate math!

Pi Day is March 14. If you write dates in the month/date format, then 3/14 at 1:59 is about as close as the calendar can get to 3.14159etc.

(Otherwise, you can celebrate Pi Approximation Day on July 22, or 22/7.)

Unfortunately, most of the activities on teacher blogs and Pinterest focus on the pi/pie wordplay or on memorizing the digits. With a bit of digging, however, I found a few puzzles that let us sink our metaphorical teeth into real mathematical meat.

What’s the Big Deal? Why Pi?

In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same.

Every circle you can imagine is the exact image of every other circle there is.

This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand upright, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters.

What makes a circle so special and beautiful? Any child will tell you, what makes a circle is its roundness. Perfectly smooth and plump, but not too fat.

The definition of a circle is “all the points at a certain distance from the center.” Can you see why this definition forces absolute symmetry, with no pointy sides or bumped-out curves?

One way to express that perfect roundness in numbers is to compare it to the distance across. How many times would you have to walk back and forth across the middle of the circle to make the same distance as one trip around?

The ratio is the same for every circle, no matter which direction you walk.

That’s pi!

Puzzles with Pi

For all ages:

Sarah Carter created this fun variation on the classic Four 4s puzzle for Pi Day:

Using only the digits 3, 1, 4 once in each calculation, how many numbers can you make?

You can use any math you know: add, subtract, multiply, square roots, factorials, etc. You can concatenate the digits, putting them together to make a two-digit or three-digit number.

For older students:

1. Imagine the Earth as a perfect sphere with a long rope tightly wrapped around the equator. Then increase the length of the rope by 10 feet, and magically lift it off the Earth to float above the equator. Will an ant be able to squeeze under the rope without touching it? What about a cat? A person?

2. If you ride a bicycle over a puddle of water, the wheels will leave wet marks on the road. Obviously, each wheel leaves a periodic pattern. How the two patterns are related? Do they overlap? Does their relative position depend on the length of the puddle? The bicycle? The size of the wheels?

3. Draw a semicircle. Along its diameter draw smaller semicircles (not necessarily the same size) that touch each other. Because there are no spaces in between, the sum of the diameters of the small semicircles must equal the diameter of the large one. What about their perimeter, the sum of their arc lengths?

4. Choose any smallish number N. How can you cut a circular shape into N parts of equal area with lines of equal lengths, using only a straight-edge and compass? Hint: The lines don’t have to be straight.

[Solutions at Alexander Bogomolny’s Pi Page. Scroll down to “Extras.”]

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

— Edward Titchmarsh

For More Information

Here are a few pi-related links you may find interesting:

Or for pure silliness:

Have fun playing math with your kids!

John Reid, CC BY-SA 3.0 via Wikimedia Commons

Happy Birthday, General Relativity

Don’t forget that Pi Day is also Albert Einstein’s birthday! And this year marks the 100th anniversary of his Theory of General Relativity. So Science Magazine has a special Einstein issue online, featuring this interactive comic:

comic-image

You may also enjoy:

Pi: Who Needs That Many Digits?

From Numberphile: Pi is famously calculated to trillions of digits – but Dr. James Grime says 39 is enough.

How you round it off makes a difference:

An extra note from Dr. Grime: “Since pi39 ends in 0, you may think we could use pi38 instead, which has even fewer digits. Unfortunately, the rounding errors of pi38 are ten times larger than the rounding errors of pi39 — more than a hydrogen atom. So that extra decimal place makes a difference, even if it’s 0.”

Pi and Buffon’s Matches

From Numberphile: Dr Tony Padilla’s unique (and low budget) twist on the Buffon’s Needle experiment to learn the true value of Pi.

For a kid-friendly version of this experiment, try throwing food:

Do you have a favorite family activity for celebrating Pi Day? I’d love to hear it!

Unending Digits… Why Not Keep It Simple?

Unending-digits

Unending digits …
Why not keep it simple, like
Twenty-two sevenths?

—Luke Anderson

Math Poetry Activity

Encourage your students to make their own Pi Day haiku with these tips from Mr. L’s Math:

And remember, Pi Day is also Albert Einstein’s birthday! Check out this series of short videos about his life and work: Happy Birthday, Einstein.

CREDITS: Today’s quote is from Luke Anderson, via TeachPi.org. Background photo courtesy of Robert Couse-Baker (CC BY 2.0) via Flickr.

Pi Makes a River Bend

From Numberphile: “Sinuosity is a measure of how ‘bendy’ a river is. It is the length of the river divided by the direct route. Featuring Dr. James Grime.”

Update

After posting this video, Dr. Grimes and Lawrence Roberts began collecting and analyzing data about real-world rivers. It turns out the pi theory of sinuosity is too simple. Read about their results: