Square root of 2 the square root of two, with a reasonable small denominator, the fraction (≈ 1.4142857) is sometimes used. The sequence in the OEIS gives the numerical value for the square root of two, truncated to 65 decimal places: The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of in four sexagesimal figures, , which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of : Another early close approximation is given in ancient Indian mathematical texts, the Sulbasutras (c. 800–200 BC) as follows: "Increase the length [of the side] by its third
Fast inverse square root to compute because this equation is equivalent to where the fraction term is the inverse square root of . At the time, floating-point division was generally expensive compared to multiplication; the fast inverse square root algorithm bypassed the division step, giving it its performance advantage. "Quake III Arena", a first-person shooter video game, used the fast inverse square root algorithm to accelerate graphics computation, but the algorithm has since been implemented in some dedicated hardware vertex shaders using field-programmable gate arrays (FPGA). The following code is the fast inverse square root implementation from "Quake III Arena", stripped of C preprocessor