Circling the square Baudhayana’s method of constructing a circle equal in area to a square Circling the square in Hindi

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Baudhayana method of constructing a circle equal in area to a square
वर्ग के क्षेत्रफल के बराबर एक वृत्त Circling the square in Hindi

वर्ग के क्षेत्रफल के बराबर एक वृत्त बनाना 

Constructing a circle equal to the area of the square

Baudhayana was able to construct a circle almost equal in area to a square and vice versa. These procedures are described in his Sulbasutra

Circling the square

finding a circle whose area is the same as that of a square (the reverse of squaring the circle).

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Draw half its diagonal about the centre towards the East–West line; then describe a circle together with a third part of that which lies outside the square.

Explanation:

  • Draw the half-diagonal of the square, which is larger than the half-side by 
    {displaystyle x={a over 2}{sqrt {2}}-{a over 2}}
    .
  • Then draw a circle with radius 
    {displaystyle {a over 2}+{x over 3}}
    , or

    {displaystyle {a over 2}+{a over 6}({sqrt {2}}-1)}, which equals

    {displaystyle {a over 6}(2+{sqrt {2}})}.

  • Now 
    {displaystyle (2+{sqrt {2}})^{2}approx 11.66approx {36.6 over pi }}
    , so the area

    {displaystyle {pi }r^{2}approx pi times {a^{2} over 6^{2}}times {36.6 over pi }approx a^{2}}.

 
YouTube Channel  : High School Maths – T K P   
 
 

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