Maths Discovery

          When I was in secondary school, I began to wonder - 'Why isnt there any formula for calculating the area of all the polygons,I had seen formulas for a square, for a rectangle but I hadn't seen any for a nonagon or heptagon'. So I decided to derive formulas for them.
         After a little work. I was able to get a formula for a regular hexagon and a nonagon. I went to show my math teacher my achievement. He told me to try to get a formula that would work for all regular polygons. I got to work and hit upon a solution. I was excited! I had thought of a problem and actually solved it.
        I noticed that as the number of sides got larger the polygon becomes more and more like a circle. And then it struck! A circle is no more than a polygon with an infinte number of sides.It was also my first encounter with the infinite. And there I was thinking of possibities, What if none had done this before? Will I get a medal or some sort of award? I was beginning to dream big. I checked the library and there was 'my'formula in the encylopaedia britannica. Someone had beat me to it. I was gutted.In the  end, It didnt really matter, I had experienced the joy of being a mathematician. I had encountered a problem and solved it. That was all that really mattered.