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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 \((\frac{6}{2+\sqrt{2}})^2 = 3.088311...\) (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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