Scientific Traditions in Hindu History

They don’t always provide proofs for mathematical formulae, or rigorous formulas for physical observations. Nevertheless, they were good philosophical observations that did have a lot of meaning aside from just voodoo.

From Baudhaayana Shulba Sutras

The Baudhaayana Shulba Sutras of the Tattiriya Shaakha, of Krisha Yajur Veda had aphorisms on the following mathematical theorems:

1. Pythagorean Theorem’s proof and Triplets
   • Proof
     • Reference: Baudhaayana Shulba Sutra > Verse 1.12
       • Shulba Sutras are rope measurement techniques
       • They deal with design of altars for religious rites
       • This part was dealing with the construction of Mahaa Vedi, a sacrificial altar
       • Measurements of Vedis and Yoopas were critical to religion, for sanctity
     • Sanskrit:
       • दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी
         च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥
     • Transliteration:
       • deergha chatursrasyaakshanayaa rajjuh paarshvamaanee, tiryagmaanee, cha yatprthagbhoote kurutastadubhayaan karoti.
     • Translation:
       • The diagonal of an oblong produces by itself both the areas which the two sides of the oblong produce separately.
   • Triplets
     • Reference: Baudhaayana Shulba Sutra > Verse 1.13

     • Sanskrit:

     • Transliteration:
       • tāsāṃ trika-catuskayār-dvādaśika-pañcikayāḥ pañca-daśikāṣṭikāyāḥ saptaka-catu-viṃśikayār-dvādaśika-pañcātriṃśikayāḥ pañca-daśikāṣṭi-triśikayārityāsu-upaladhāḥ
     • Translation:
       • This verse basically lists out a bunch of values for which the rule had been found to hold. These include (3, 4), (12, 5), (15, 8), (7, 24), (12, 35) and (15, 36).
2. Digits of $\pi$
   • It was calculated as $(\frac{6}{2+\sqrt{2}}{)}^2=\mathrm{3.088311...}$ (no decimal points right)
   • They tried to use some patterns, but indeed, $\pi$ is irrational.
3. Circling the Square and Squaring the Circle

Others

Reference: https://arohipublications.com/?p=2228 (Translation from Sanskrit to English)

• Acharya Bharadwaj (son of Acharya Brihaspati)
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    • It’s Ion Engines, claims: Vedic Ion Engine | Volume 4, Issue 3, September 2014 | IJEIT