You have listed three often-used methods of solving problems. Yes, there are many more. First, let’s realize what’s really happening:
Step 1 --> Step 2 [we don’t need any method]
Step 1 --/no /--> Step 2 [we need another path]
The impasse may be because of time, space, money, or many other reasons. For example, we used to wait in long lines at banks before automatic deposit, ATM's and on-line banking were introduced. Many slow or costly processes are now “automated.”
So, the “workaround” is to introduce a different step, Step 3, that gets us to Step 2 by a different path:
Step 1 --/ no /--> Step 2
| A
V |
---- Step 3 -----
In math, one way we do this is using equations or inequalities. For example, I don’t need to count John’s money if I know that he gets paid $10 for each hour of work; just tell me how many hours he worked.
More complicated functions (like John getting paid $15 for overtime) require piecewise functions.
To make equations and inequalities easy to understand, we use plots or graphs.
These and other solution methods are called “models.”
Statistics has lots and lots of models. The normal (or bell-shaped) curve is an often-used one.
Then, with computers, we use simulation or virtual reality. In object-oriented programming, a portion al a program is created that takes input just like a real object (say, elevator buttons) and produces output just like that real object (say, what floor the elevator is currently on).
Have you sat in a car driving simulator?? It shows the picture of the road, has a steering wheel and a gas pedal and … and a car crash simulation is much faster and less expensive that crashing a real car.
Everything from trips to Mars to mining to medical operations now have very good virtual reality systems to model or simulate them. A computer can be like a pre-school "sandbox," but where (1) it doesn’t cost much, (2) nobody gets hurt, and (3) it’s o.k. to fail – that’s especially important in something like a flight simulator.