How To Solve It by George Polya

modified 20/04/2024 22:38

There are 4 phases to solving a problem:

Undestanding the problem.
- ask the questions “What is the unknown?”, “What is the data?”, “What is the condition?” “Is it possible to satisfy the condition?”
- look at the unknown and try to find a problem with a similar unknown; introduce new notation (variables names for lengths, etc)
- draw a figure, and point out the unknown and the known on it
Seeing how the items are connected (how the unknown is linked to data), in order to make a plan.
- ask the question “Do you know a related problem?”
- if you find any, try to solve them first
- restate the problem; go around in circles, adding new stuff just to make the problem simmilar to other problems you may have solved in the past
Carrying out the plan.
- understand if you can see that the step is correct VS prove that it is correct
Looking back at the completed solution, reviewing and discussing it.
- check the result; make sure you used all the data;
- check the arguments; make sure you can prove them
- ask “Can you derive the result differently?” “Can you see it at a glance?”
- create some tests; try some other values, and make sure that the results change accodingly
- finally, ask “Can we use the result or method for some other problem?”