Some equations cannot be solved by analytical methods such as factorisation. Instead an iterative method is used to find a sequence of numbers that converges to a solution. Any term in the sequence provides an approximation to a solution and, the more terms that are taken, the better is the approximation.

Newton's method (Newton-Raphson) is one such method. It also works for complex numbers with interesting connections to fractals.

activity pages

• Numerical methods of solving equations - one point iterative methods
• Numerical methods of solving equations - sequence graphs and web plots
• Numerical methods of solving equations - Newton's method
• Numerical methods of solving equations - Newton's method - complex numbers - Newton Basins
• Numerical methods of solving equations - Newton's method - Why it is so good?

• compare different methods - Nicholas Exner.
• Newton's method illustration 1
• Newton's method illustration 2 - Paul Garrett
• Newton's method calculator (includes graph and tangents)
• example of Newton's method not working - Paul Garrett
• Newton's method calculator - Steven Tschantz

• Newton's method for finding square roots is the same as the "divide and average" algorithm.
• donkey grazing in half a circular field
• How do you solve the equation x^x = 100?

Newton Basins/Fractals - Newton's method applied to finding complex solutions

• Newton Basins - David Joyce

Dynamical Systems software
Newton basins (NB. Save feature does not work.)