How many rectangle triangles do you know that have integer size sides?

When I was a child, some time after I have learned about Pythagoras theorem and a little trigonometry, I became completely fascinated by math. It is not to say I was brilliant in it. Even when I was probably above the average, the issue was that I was really fascinated. As expected, very soon I got the book "The Man Who Counted" in my hands. In the beginning it wasn't me, but my mother who read the short stories in loud voice.

I had of course some other people that influenced in my taste for math. Among them was my father, also one of his friends, Luis Fornero, and finally my first year math teacher in the secondary school, professor Nadal.

By the middle of that first year, my schoolmates already called me Pythagoras. As before, I think the issue wasn't that I was brilliant in anyway, but because I was fairly annoying. I got my fame for telling my fellows about some mathematical curiosities they didn't want to know about, like the golden section, the Fibonacci series, the Tartaglia's triangle, and some integer size rectangular triangles besides the classic 3-4-5.

During my years in the university my performance in math was also above the average (even when I didn't get above average scores in two of the exams I had). But by the time I already knew that I was just a computer programmer with a taste for math.