Understanding formulas, shapes, algorithms etc
It is sometimes hard to... understand. To look at a formula and not "understand" it is like a torture for me. The questions that run around in my mind are: "Is it proven/Where does it come from/How can I imagine it, if possible" etc...
About the proof of a formula I can bring an example from my own schoollife:
Today, we solved an exercise about a cone and in the end, the teacher asked us: "Do you have any questions". I asked: "I'd like to see the proof for the formula ( V = 1/3*S*H) (I am in the 9-th grade)." But he said that the formula is too hard to prove at the moment - due to my knowledge about geometry.
Believing a formula without a proof for its correctness is a real torture for me...
How do you cope with formulas, that you have not seen a proof for?
Now, what about imagining a formula?
Let's take a "simple" one:
S = a * b
It's for calculating the area of a rectangle.
We are all different personalities and we all think in our own unique way and our imaginations are different too...
When I try "imagine" how the formula works, I think of 2 sides... Then I "multiply" one side with another and the other 2 sides of the rectangle form in front of my eyes.
That was an easy one.
But now, let's take a "harder" formula: A = I * I * R * t (Physics. The work that the electric field does).
I mean, how do I imagine I * I? How do I imagine I * I * R? multiplied with time!?
Even if you are able to imagine it, imagine formulas that you can't imagine :D!
How do you deal with that?
Do we even need to be able to "imagine" a formula?
For me, it's a real torture to live without a proof and/or "imagination" - it goes for all the areas that i have mentioned in the topic of this non-programming-related post.
And what is understanding afterall?
thanks for your time...