Table of Contents

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).

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 $x={a over 2}{sqrt {2}}-{a over 2}$ .
Then draw a circle with radius
{displaystyle {a over 2}+{x over 3}} ${a over 2}+{x over 3}$ , or

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

{displaystyle {a over 6}(2+{sqrt {2}})} ${a over 6}(2+{sqrt {2}})$ .
Now $(2+{sqrt {2}})^{2}approx 11.66approx {36.6 over pi }$ , so the area

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