A Mind of Doubts

Get the concepts clear, in the first place.

1. Square roots best represents the number line. Because the line cannot have thickness. In other words squares are not possible in the number line.
2. Frankly, only a growth from 1 to 2 is what matters. I feel root 2, root 3 and root 4 (2) is the real growth from 1 to 2.
3. Once 2 is formed, then 4, 8, 16, 32, 64 etc. with many many numbers contained within them happens.
4. What changes from 2 to 4 is the spin and usage of hands or machines or any other such device which can make this happen.
5. Lot many numbers are behind this. Irrational numbers, real numbers, rational numbers, natural squares and prime numbers to name a few.

I had doubts on why be irrational. This doubt is the first figure drawn by me on Windows Paint.

The second figure is the answer. I have got this picture from internet and have used it here.

This finishes off my theoretical doubts. Practicality is however different. 

Mathematicians say e is real. This is shocking to me as all men are not same in India.