Draw a circle. Draw the radius. Make a square out of one of the radii. How many of those squares do you think would fit inside the circle?

This fascinating relationship reveals a fundamental constant of the universe. The area of a square is found by multiplying its side length by itself. In this case, the square's side is the circle's radius (r), so its area is r-squared (r²). The formula for a circle's area is A = πr². This means the circle's area is precisely the area of the radius-based square multiplied by pi. Therefore, you could fit just over three of those squares—about 3.14159 of them—inside the circle.

This special number, pi (π), is a constant that relates a circle's circumference to its diameter. For any circle, no matter how large or small, the distance around it is always about 3.14 times the distance across it. Ancient mathematicians, like Archimedes, figured this out by comparing circles to polygons with many sides. They discovered this fixed ratio, which we now call pi.

Pi is an irrational number, which means its decimal representation never ends and never repeats. People have used supercomputers to calculate trillions of digits of pi, and still, no repeating pattern has been found. So, while you can easily visualize the three full squares fitting inside the circle, that extra fractional part, 0.14159..., represents a sliver of area that goes on infinitely without repetition, a simple yet profound concept in mathematics.