Independence Day and the Geometry of Fireworks

Firework bursts are often spherical, but the trails of sparks follow parabolic arcs under gravity. Each star is a projectile: its horizontal motion is uniform, vertical motion accelerates at g. The resulting curve is a parabola – the same shape that appears in satellite dishes and suspension bridges. The timing of bursts is controlled by fuses that burn at constant speed, a linear function. Mathematics predicts where each spark will land, ensuring safety distances. Even the most chaotic display follows equations Newton wrote in 1687.