The joy of mathematical thinking.

Playing on a calculator, I multiplied the constant pi times a random large number. The strange thing that happened was that I didn't see a decimal. I quickly checked the settings on my calculator and found the missing decimal places, due to rounding up from four decimals. The thing that dawned on me is that I knew there should never be an integer answer to multiplying any rational constant by pi, (except zero). 

It was at this time I realized the beauty of understanding a concept and the depth of how understanding changes your perception of the world. Funny how such a simple happening can have such a profound impact when you are paying attention.