A pentagon iteration. Connecting alternate corners of a regular pentagon produces a pentagram which encloses a smaller inverted pentagon. Iterating the process produces a sequence of nested pentagons and pentagrams.

Iteration in mathematics may refer to the process of iterating a function i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviours and difficult problems – for examples, see the Collatz conjecture and juggler sequences……..

Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton’s method is an example of an iterative method……….

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