getting started considerfor examplefinding the square root of set to some arbitrary valuee we decide that * is not close enough to set to ( / )/ we decide that * is still not close enough to set to ( )/ we decide that * is close enoughso we stop and declare to be an adequate approximation to the square root of note that the description of the method is sequence of simple stepstogether with flow of control that specifies when each step is to be executed such description is called an algorithm this algorithm is an example of guessand-check algorithm it is based on the fact that it is easy to check whether or not guess is good one bit more formallyan algorithm is finite list of instructions that describe computation that when executed on provided set of inputs will proceed through set of well-defined states and eventually produce an output an algorithm is bit like recipe from cookbook put custard mixture over heat stir dip spoon in custard remove spoon and run finger across back of spoon if clear path is leftremove custard from heat and let cool otherwise repeat it includes some tests for deciding when the process is completeas well as instructions about the order in which to execute instructionssometimes jumping to some instruction based on test so how does one capture this idea of recipe in mechanical processone way would be to design machine specifically intended to compute square roots odd as this may soundthe earliest computing machines werein factfixedprogram computersmeaning they were designed to do very specific thingsand were mostly tools to solve specific mathematical probleme to compute the trajectory of an artillery shell one of the first computers (built in by atanasoff and berrysolved systems of linear equationsbut could do nothing else alan turing' bombe machinedeveloped during world war iiwas designed strictly for the purpose of breaking german enigma codes some very simple computers still use this approach for examplea four-function calculator is fixed-program computer it can do basic arithmeticbut it cannot for simplicitywe are rounding results the word "algorithmis derived from the name of the persian mathematician muhammad ibn musa al-khwarizmi