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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

## 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).

Related  बौधायन त्रिकोणमितीय फलन Baudhayan Trigonometric Function TRIGONOMETRY DEVELOPMENT IN ANCIENT

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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