Prototype 2
Big Numbers get even Bigger Results when Multiplied

The set of numbers in Box A shows that when you square numbers (multiply each number by itself) that the results get proportionately larger with larger numbers.

Each number of the set (1 through 5) is squared resulting in the set 1, 4, 9, 16, and 25. Notice the difference between the square of 1 and 2 (their squares are 1 and 4) is 3. Whereas the difference between the squares of 4 and 5 (their squares are 16 and 25) is 9. The important characteristic is the difference between the original numbers were the same (1) while the difference between their squares are 3 and 9 respectively. The rate of change is proportionately larger for larger numbers. That is, they get bigger quicker.

This is the second prototype is that the results of squaring large numbers be disproportionately larger than squaring small numbers.


One more example might be helpful to solidify this second prototype. Add 1 to 5 and you get 6; multiply 6 times 6 and the result is 36; the difference between 25 (5 X 5) and 36 (6 X 6) is 11. So once again the "squared numbers get bigger, faster." It will happen all the way to infinity.