## 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

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

Or for pure silliness:

Have fun playing math with your kids!

## How Will You Celebrate this Epic Twosday?

Tomorrow is Tuesday 2/22/22 (or 22/2/22, if you prefer). What a wonderfully epic Twosday!

Here’s a puzzle your family or class may enjoy…

### The “All 2s” Challenge

Use only the digit 2, and try to use as few of them as you can for each calculation. You may use any math operations you know.

For example:
0 = 2 − 2
8 = 2 + 2 + 2 + 2

• Can you find a way to make 8 using fewer than four 2s?
• What other numbers can you make?
• Can you calculate all the numbers from 1–20? 1–100?

### Putting 2 in Perspective

You might enjoy practicing your math art skills with this 2-digit challenge from Steve Wyborney.

How many blocks make the digit 2? How did you count them?

Once again, the delightful Nrich Maths website offers a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity.

Click the images below to visit the corresponding December Math Calendar pages.

### For Primary Students

Here are twenty-four activities for elementary and middle school, one for each day in December during the run-up to Christmas.

When you get to the Nrich website, click a number to go to that day’s math.

### For Secondary Students

Here are twenty-four favorite activities for middle and high school, one for each day in December in the run-up to Christmas.

When you get to the Nrich website, click a number to go to that day’s math.

### More Holiday Math

I encourage you also to explore my HUGE holiday math post:

Or check out these pages for more ideas:

Have fun playing math with your kids!

CREDITS: “Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

## Did You Get Your Playful Math?

My February playful math newsletter went out yesterday morning to all subscribers.

This month’s issue featured a couple of string art projects for Valentine’s Day, the cardioid curve, make-your-own math art, and the link between string art and calculus.

Not a subscriber? Don’t miss next month’s playful math activities! Click the link below to sign up today, and we’ll send you our free math and writing booklets, too.

As a Bonus: You’ll receive my 8-week email series “Playful Math for Families” and be one of the first to hear about any new books, revisions, and sales or other promotions

## Happy Mathy Hanukkah

Hiding among all the other winter-themed activity ideas, I found a few posts for those who celebrate the Festival of Lights.

### For More Holiday Math

CREDITS: Candle photo (top) by Enrique Macias via Unsplash.com.

## Mathy Christmas Cards

I always wait too long to put cards in the mail. Maybe these creative beauties will inspire me to get started right away?

### For More Holiday Math

CREDITS: Reindeer photo (top) by Norman Tsui via Unsplash.com.

## Mathematical Days of Christmas

Enjoy this bit of seasonal fidgeting from Vi Hart.

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and relish the fun of learning something new.

### For More Holiday Math

CREDITS: Lamppost photo (top) by Aaron Burden via Unsplash.com.

## Have a Mathematical Thanksgiving Dinner

With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

### And for Dessert

May I suggest some of Don Cohen’s Infinite Cake?

CREDITS: “Thankful” photo (top) by Pro Church Media via Unsplash.com. Food videos by mathemusician/doodler Vi Hart.

## Happy Hamilton Day (Belated)

While searching for posts to add to the Playful Math Carnival, I stumbled on a new-to-me math holiday.

Hamilton Day celebrates mathematical discovery — that “Aha!” moment when your eyes are opened and you see something new.

Or something new-to-you. That’s worth celebrating, too.

### History of Hamilton Day

Irish mathematician William R. Hamilton was struggling with a tough math problem in October, 1843. It had him stumped. Then on the 16th, as he walked along Dublin’s Royal Canal with his wife, inspiration struck.

He suddenly realized he could look at the problem from a new direction, and that would make everything fall into place.

“And here there dawned on me the notion that we must admit, in some sense, a fourth dimension of space for the purpose of calculating with triples … An electric circuit seemed to close, and a spark flashed forth.”

—Sir William Rowan Hamilton

In one of the most famous acts of vandalism in math history, Hamilton pulled out a knife and scratched his new equation into the stone of the Broome Bridge: i² = j² = k² = ijk = -1.

### Also by Hamilton

“Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?”

—Sir William Rowan Hamilton
quoted in H. Eves, Mathematical Circles Revisited

### Why Celebrate Hamilton Day

“So there’s much to celebrate on Hamilton Day. Beyond its utility, we can appreciate mathematics as a human endeavor, with struggles and setbacks and triumphs. We can highlight the opportunity math affords for daring, creativity, and out-of-the-box thinking.

“Hamilton Day could, in other words, pivot away from Pi Day’s gluttony and memorization, neither of which is part of mathematics, toward the intellectual freedom and drama that are.”

— Katharine Merow
Celebrate Hamilton Day, a Better Mathematical Holiday

### How Will You Celebrate?

• Learn about a new-to-you math topic.
• Work on a tough math problem.
• Think about different ways to do things.
• Try a nonstandard approach.
• Talk about how it feels when you learn something new and it finally makes sense.

I’ve penciled Hamilton Day (October 16) into my calendar for next year.