For me geometry is one of the most imaginative and creative part of mathematics. I always thought that because you need to work with all those instruments everything is like drawing a painting. And the most important thing is that if you do not do it carefully and patiently then everything will be wrong, and you will never understand the problem correctly. The first time I saw a triangle I though what a simple thing, but in the end everything became hard, even that triangle. All the things started to become complicated starting from a point and I remember my teacher saying: “if you cannot see the picture in your mind, you will never understand it and do it on the blackboard”. I was frustrated when he said that because most of the time I had problems with trying to imagine all the things.
The most important problem for me in those days was the PARALLELS. I have never understood the definition : “ parallel straight lines are straight lines that, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction” (this is definition 23 from Book I of Elements by Euclid). Of course this was not the definition the teacher told us, but it was similar. The thing that I did not really understand was the fact that the line never meet. I know that when the teacher drew them it seemed right, but I was always confused by the fact that maybe something happens and in their way to infinite the lines will meet. Because I straggled with this definition it was hard for me to understand some points. So I stopped thinking about this one and decided that I need to believe my teacher and that will do it.
And now, the first book I took from the library to read in my first year at university it was about geometry. I thought that maybe now I will understand the things better. And I did it. I found exactly the thing I needed to find. The non-Euclidean geometry was the thing that maid me understand the geometry I did in school. And I cannot wait to read more and understand more.
I know that I am not an expert at non-Euclidean geometry, but if you would like to read more about it let me know and I will give you some personal opinions about it.