Pi: In the Sky, on Earth and at the Library of Congress

This post is by Ralph Pantozzi, a 2024–2025 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

Have you encountered a circle today? Humans have long been fascinated by the fact that the circumference (distance around a circle) of any circle measures approximately 3.14 times the length of its diameter (distance of a straight line connecting two points on the circle and passing through the middle). The length of the circumference of a circle divided by the length of its diameter is the number we call π. In 2009, the House of Representatives agreed to a resolution recognizing March 14 as “Pi Day” to teach students about the “constant that has been studied throughout history and is central in mathematics as well as science and engineering.”

As a child, I was mesmerized by circles in the sky and on the ground, from the orbits of planets to the spaceships and telescopes we used to explore the solar system. As a math teacher, I’ve enjoyed teaching students about circles and π for decades. During my Albert Einstein Distinguished Educator Fellowship, I’ve discovered even more circles in Library of Congress primary sources, like the metallic circle of recorded music whose duplicate is now in deep space. In this blog, I’ll highlight a variety of circles in the Library’s collections and suggest some opportunities for you to examine the circles that are all around you. 

Circles in Our World  

Objects in nature, like sunflowers, that grow outward from a center point will often form circles. Think about where else you might find circles in the natural world, and why the object may have taken that shape.

Our world is also full of circles made by humans. You’ll find them in buttons, gears, pulleys and even irrigation patterns. Where else can you find circles in human-made objects? Does the circular shape serve a practical purpose?

Circles and Travel

Wheels are circles that serve many practical purposes, including putting us in motion. One might even say that circles “make the world go ‘round”.  Wheels help us move in cars, on bicycles, and in wheelchairs and scooters.

Airplanes use circles too. In the air, the circular propellers of the engines push the plane forward. And as planes travel, pilots will navigate the “great circle route,” a path that follows a slice of Earth that cuts the globe exactly in half. There is no wasted distance when one travels a perfect great circle route through the air. While this line looks straight on the map below, it is in fact a piece of that circle.

Try using a string on a flat map to connect any two locations on the map. Then, connect the same two locations on a globe, using the least amount of string. Does the string pass over the same points in between? You’ll find the answer is no, because Earth’s surface is not flat.

From Play to Calculation

Back on the ground, humans form circles themselves, sometimes rotating around a center, like on the playground. The giant stride was a popular ride in the early 20th century that allowed kids to run around in circles holding chains. The kids would take off flying – and sometimes fall off – the until the ride was retired due to safety considerations. What (safer) circles do you use or find on playgrounds, amusement parks, in board games or on fields?

Humans discovered the value of π through play and some calculation. Inspired by a spin around the giant stride, here’s a way to estimate that the value of π is near 3 with your own body.

1. Measure the length of your arm with your shoe. How many shoes long is your arm? (It might be, say, 2 ½ shoes long.)
2. Write this number down and put your shoe back on.
3. Double this number: it will be the diameter of the circle you’re about to walk.
4. Find a vertical pole-shaped object that is at least as tall as your shoulders. (Use a broom or an actual street or playground pole that you can walk around.)
5. Hold onto the pole and straighten your arm, parallel to the ground.

   

6. Mark the location of the back of your shoe.
7. Walk, one foot after the other, in a full circle around the pole, keeping your arm straightened, and count your steps.
8. The number of steps that you counted is the circumference of the circle.
9. Write this number down.
10. Divide the circumference of the circle (the number of steps) by the diameter (twice the length of your arm).

Everyone who tries this, regardless of the length of their arm, will get an answer of approximately 3. That’s a rough estimate of the value of π. 

You can also conduct this experiment with any existing circle, small or large.

1. Lay a string across the diameter of the circle. (Do your best to make sure your string passes through the center of the circle, as that is where the diameter lies.)

   

2. Cut the string to the length of the diameter.
3. Lay your string around the circumference of the circle, as shown in the photo below.

   

4. Mark the beginning and the end of the string.
5. Continue to lay the string around the circumference to cover the whole distance around.

You’ll find that it takes more than three string lengths (three diameters) to go around your circle. You’ve shown that π, the ratio of the circumference to the diameter, starts with the number 3.

Coming Full Circle

Consider the original Ferris wheel, which made its debut at the World’s Columbian Exposition (also known as the Chicago World’s Fair) in 1893. It was 264 feet tall. As the circumference of any circle is always (approximately) 3.14 times the diameter, the ride around the wheel took passengers a distance greater than the height of the Washington Monument. What’s the largest circle you’ve ever traveled around? 

For a while, Chicago residents imagined they were at the center of the universe, with everything measured from their location, as in this pre-exhibition advertisement.  

Like the Chicago residents of 1893, humans once believed that Earth was at the center of the universe, and that everything revolved around our planet. Later, we began to accept that perhaps the sun was the center. Both models turned out to be wrong, but human curiosity has driven us to discover the facts and reach for the stars.

A bit more accuracy about the digits of the number π is needed in order to send spaceships out into circular orbits, and so humans have continued to calculate the value of π with greater accuracy. Currently, we can calculate trillions of the digits of π. The first 100 digits, in case you were wondering, are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. 

I hope this post has your gears turning, and not simply going in circles. On this Pi Day, take time to notice circles, in your world, and at the Library of Congress. The circumference and the diameter are always connected by the number π. It doesn’t matter how many digits you happen to know.