In high school, we learnt that the area of a circle is Pi (π) times square of its radius(r). I had no clue as to the origin of this formula (π• r squared). All of us learnt it by rote. It was a fundamental formula someone discovered, we rationalized.Just as the formula for the area of a square whose each side equals r is (r times r).
However, recently I spent some time thinking upon this formula and the mystery unfolded. The formula doesn't seem that mysterious now. If you draw a square with each side equaling 2r, which contains four equal squares with each side r , then the area of the circle with radius r inscribed within will be slightly bigger than the area of three of these squares. Actually, the area of this circle will be 3.1416 times the area of a single square of side r! That is the original formula we mentioned in first para, where the number 3.1416 is represented by the special character π.
With this information we can deduce the areas of squares and circles much easily. If we know the area of square then the area of the circle inscribed within is 78.54 % of the area of that square.
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