Pi
Pi is the number you get when you divide any circle's edge length by its width.
Wrap a string around a round cake, then measure straight across the middle. The string around the edge is always about 3.14 times the width across. Every round cake gives this same number, no matter its size.
Explaining pi by grade level
Draw a circle and measure all the way around it with a string. Then measure straight across the middle. The string is always about three times longer than the line across. That number, a bit more than three, is pi.
Projects that explore pi
Pi is the number you get when you divide any circle's edge length by its width. One way to close in on that ratio is to wrap polygons tighter and tighter around a circle. You start with a square, then double the sides to 8, then 16, and so on. Each polygon's perimeter gets closer to the circle's circumference, producing a value that approaches pi from above.
Because pi equals a circle's edge length divided by its width, any polygon drawn inside or around a circle gives an approximate value. Ancient math used exactly this approach — inscribed and circumscribed shapes whose perimeters bracket the true value. The more sides the polygon has, the closer the estimate gets. You can track how fast the improvement happens by comparing errors from polygons with different side counts across six different pairs. The error ratio follows a clear pattern: as the side count grows, it approaches the square of the inverse of the side-count ratio, meaning the error shrinks in a predictable, measurable way.