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Three well-known algorithms, implemented separately within a span of 20 years, demonstrate the use of mathematics developed hundreds of years ago. The algorithms don't have much in common except for two things: they were implemented between 1949 and 1965 during the so-called first generation of computing hardware-and they are good examples of rigorous thinking. First, I explain Bresenham's algorithm and apply it to a fundamental process of computer graphics-drawing a line on a raster screen. Second, although there are several ways to calculate a square root, the square root algorithm is interesting because it takes advantage of hardware design. And, finally, while the calculation of n goes back more than 2,200 years, Machin's algorithm from 1706 is of importance to the history of computing.