Hero method

This technique extracts the square root from a positive number a. In other words, solving the equation x²=a for x or search for the zero of the function f(x)=x²-a . The method is iterative and geometric. The idea is to search for rectangles getting closer to a square, all of whose surface areas are equal to a.

Hero method

Newton-Raphson method

From a geometric point of view this method substitutes a sequence of straight lines to the curve of a function we are searching for a zero. These lines are tangents, the best local linear approximation to the curve. The first tangent line is an important choice.

Newton-Raphson method

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Thanks to Chao-Kuei Hung and Richard O'Keefe for the reviews of the article below.