Baudhayana Shulb(शुलभ) sutra or shraut(स्रोत) sutra

Bodhayan

The Hindi meaning of the Sanskrit word Shulb is the rope of measuring. The Shulb Sutras are part of the Vedic Shrauta Sutras which are part of the Vedas. The word Shrut is derived from the word 'Shruti', in which the sources have been compiled in connection with the rituals of the Vedic rituals, the place selection of Havan, temples, etc., the construction of the Vedika, the measurements etc. The Shulb Sutras are the formulas of Indian geometrical or, say, the oldest sources of modern geometric.

   

 

There are 8 Shulab Sutras available right now. Which are as follows: -

1. Apastamb Shulab Sutra

2. Boudhayan- Shulb Sutra

3. manav Shulab Sutra

4. Katyan Shulab Sutra

5. Maitrani Shulab Sutra

6. Varah (in manuscript form)

7. Vadhul (in manuscript form)

8. Hiranyakeshin

The Boudhayan Shulb Sutra contains important formulas of geometry in which the famous Boudhayan theorem, known in the modern era as the Pytha Gores theorem: -


In one sutra, Baudhayana stated the rule of the square of the diagonal of a rectangle.

दीर्घस्याक्षणया रज्जुः पार्श्वमानी तिर्यकं मानी च।यत्पृथग्भूते कुरुतस्तदुभयांकरोति ॥

The value of the area (square) of the diagonal (raju) of the long chaturas


The highest evidence of the truth of the Buddhist theorem is available, on whose test this true percentage is proved to be true.


Construct a circle equal to the area of ​​the area of ​​the square.
(Square of area equal to the area of the Circle building)

(rectangles) is the sum of the squares of the base (lateral) and triang

amani (perpendicular).

चतुरस्रं मण्डलं चिकीर्षन्न् अक्षयार्धं मध्यात्प्राचीमभ्यापातयेत्। यदतिशिष्यते तस्य सह तृतीयेन मण्डलं परिलिखेत्।

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.
If the side of the square is 2a, then the radius of the circle is r = a


Made the square of the area equal to the area of ​​the circle.(Circle of area equal to the area of the square built)

मण्डलं चतुरस्रं चिकीर्षन्विष्कम्भमष्टौ भागान्कृत्वा भागमेकोनत्रिंशधा विभाज्याष्टाविंशतिभागानुद्धरेत् भागस्य च षष्ठमष्टमभागोनम् ॥

If you wish to turn a circle into a square, divide the diameter into eight parts and one of these parts into twenty-nine parts: of these twenty-nine parts remove twenty-eight and moreover the sixth part of the one part left less the eighth part of the sixth part.

Apastamb Shulb Sutra: -

It is named in the Taittiriya branch of Krishna Yajurveda. This book is divided into 30 questions. In the first 24 questions there is a law of Vedic Yajna. The 25th question has a definition, proverb, and it's mantras. The 26th and 27th questions describe religious works. The 28th and 29th questions are popularly known as house questions, here is a description of the measurement and the geometry of the altars, which are found even today in the form of indian architecture.

समस्य द्विकर्णि प्रमाणं तृतीयेन वर्धयेत। तच् चतुर्थेनात्मचतुस्त्रिंशोनेन सविशेषः।

To get the value of a square's diagonal by adding one-third to its arm, then adding one-fourth of it, then subtracting it from the 34th part of its arm, what is found is approximately the value of the diagonal.

2 ≈ 1 + 1/3 + 1/ 3 ⋅ 4 − 1/3 ⋅ 4 ⋅ 34 = 577/408 ≈ 1.414216