Bresenham's line algorithm
Draws a straight line on a pixel grid using only integer addition — no floating point, no division.
Jack Bresenham devised it in 1962 at IBM for a Calcomp plotter and published it in 1965. The trick is an error term that accumulates step by step: for each pixel along the dominant axis, the sign of the error decides whether the other coordinate advances or holds. Everything is addition, subtraction and comparison — operations even 1960s hardware ran fast.
The midpoint circle variant draws circles the same way, and the principle survives in everything from font rasterization to the line tool in pixel editors. The dry truth is that nearly every straight line you have seen on a screen passed through Bresenham's error term.