Maths Puzzle : Prove


Prove that 3 < π < 4 .


6 Responses to “Maths Puzzle : Prove”

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  4. 4 Gp July 12, 2006 at 6:41 pm

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  5. 5 S.Karthikeyan July 11, 2006 at 10:54 am

    In the same line.

    Consider a circle of radius r. Consider another square of length 2r around the circle. Here r = 1 unit.

    Area of square r*r i.e 4 unit square.
    Area of circle pi*r*r = pi unit square.

    By observation 4 > pi.

    Simillarly consider a square of length root of 3.

    Area of suqare will be 3 unit square wich is less than Area of circle.

    i.e we have 3 < pi < 4

  6. 6 shocking July 11, 2006 at 9:56 am

    pie, by defination is the ratio between the circumference of a circle and diameter.

    take a hexagon of side a, by observation you know its circumference (= 6a) is less than that of the circle of radius a.
    pie >3

    now take a square of side 2a. its circumference is more than that of the circle

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