Irrational Numbers

Have you ever tried to tell a story that goes on forever and ever, with no end in sight? A story where every single part is brand new and never, ever repeats itself? That's a little bit like me. I'm a number, but I’m not like the neat and tidy ones you line up in your math class. I'm a little bit wild, a little bit messy, and I go on for infinity. You can’t write me down as a simple fraction, like one-half or three-quarters. If you try to write me as a decimal, your pencil will run out of lead before you can finish, because I have no end. I love to hide in plain sight. Can you imagine a perfect square, with four equal sides? I’m hiding in the diagonal line that stretches from one corner to the opposite one. Do you see circles all around you, from the wheels on a bus to the pizzas you eat for dinner? I’m there too, hiding in the beautiful, perfect curve of every single one. I am a secret that numbers have been keeping for a very long time.

My story really begins a long, long time ago, in the 5th century BCE in ancient Greece. There was a group of very smart people called the Pythagoreans. They were led by a famous thinker named Pythagoras, and they absolutely loved numbers. They believed that the whole world, from the stars in the sky to the music they played, could be explained using simple, whole numbers and their fractions. They thought numbers were perfect, predictable, and orderly. But one day, one of their members, a curious man named Hippasus of Metapontum, found me by accident. He was studying a simple square, one where each side was exactly 1 unit long. He wanted to figure out the length of the diagonal line. Using a special rule his group had discovered, the Pythagorean theorem, he calculated the answer. The length of that line was the square root of 2. When he tried to write it down as a number, it started out as 1.41421356 and then… it just kept going. And going. And going. There was no pattern. It never repeated. It was me. This was a huge shock. I didn't fit their perfect rules. A number that couldn't be a neat fraction? It seemed impossible. According to legend, this discovery was so startling and so disruptive to their beliefs that they tried to keep me a secret from the whole world. I was a number that broke all the rules.

For a long time, I was just a strange mathematical secret. But it turns out, I'm not the only one of my kind. My family is called the Irrational Numbers. My most famous friend, the superstar of all numbers, is Pi. You've probably heard of Pi. Pi is the special number you find in every circle. If you take the distance all the way around a circle, called the circumference, and divide it by the distance straight across its middle, called the diameter, you always get Pi. And just like me, Pi is irrational. It begins with 3.14159, but its digits march on forever without ever repeating. Pi is incredibly important. People use it to design everything from car tires to spaceships. Without Pi, we couldn't understand how planets orbit the sun. I have other amazing relatives, too, like the golden ratio, which shows up in nature. You can see its beautiful, spiraling pattern in the curl of a seashell, the seeds of a sunflower, and even in the shape of giant galaxies. We irrational numbers are hiding everywhere, adding a little bit of infinite mystery to the world.

Today, you don’t have to keep me a secret. In fact, people use me and my irrational friends all the time. Scientists use us to understand the universe, and engineers need us to build strong bridges and amazing machines. The artists who create the cool computer graphics you see in movies and video games use our endless patterns to make things look more realistic. My story shows that sometimes, the things that seem messy or that break the rules are the most interesting discoveries of all. I am proof that there is always something new to learn and that the world is filled with infinite wonder. So stay curious, keep asking questions, and remember that even in a simple square or a perfect circle, there might be a secret story that goes on forever.