Pythagorean Geometry in Vedic-era Texts

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    In Context

    • The position paper, part of Karnataka’s submissions to the NCERT for a National Curriculum Framework, describes Pythagoras’s theorem as “fake news”.

    About

    • The Pythagoras theorem is disputed in many international forums. Not the content, but Pythagoras claiming it as his own.
    • It has referred to a text called the Baudhayana Sulbasutra, in which a specific shloka refers to the theorem.

    Pythagoras: Theorem named after him

    • Evidence suggests that the Greek philosopher (around 570–490 BC) did exist. However, there is an element of mystery around him, largely because of the secretive nature of the school/society he founded in Italy. 
    • Relatively little is known about his mathematical achievements, because there is nothing today of his own writings.

    Pythagoras Theorem

    • The Pythagoras theorem describes the relationship connecting the three sides of a right triangle (one in which one of the angles is 90°):
      • a² + b² = c²
      • where a and b are the two perpendicular sides, and c is the length of the diagonal side.
    • If any two sides of a right triangle are known, the theorem allows you to calculate the third side. Extended to the sides of squares and rectangles and their diagonals, the equation is of immense importance in construction, navigation and astronomy.

    How do we know that Indian mathematicians from the Vedic period knew this?

    • There are references in the sulbasutras, which are texts pertaining to fire rituals (yajanas) performed by Vedic Indians. The oldest of these is the Baudhayana Sulbasutra.
      • The period of Baudhayana Sulbasutra is uncertain. It is estimated based on linguistic and other secondary historical considerations.
    • In recent literature, Baudhayana Sulbasutra is taken to be from around 800 BCE.
    • Baudhayana Sulbasutra contains a statement of what is called Pythagoras theorem (it was known rather as a geometric fact, and not as a ‘theorem’).
    • The yajna rituals involved construction of altars (vedi) and fireplaces (agni) in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles.
    • The sulbasutras describe steps towards construction of these figures with prescribed sizes.

    Image Courtesy: IE

    How did the Knowledge of Equation Evolve?

    • The earliest evidence is from the Old Babylonian civilisation (1900-1600 BCE).
    • They referred to it as the Diagonal Rule.
    • The earliest evidence of a proof comes from a period after the sulbasutras.
    • The oldest surviving axiomatic proof of the theorem is in the Elements of Euclid from around 300 BCE.

    Veda

    • About:
      • A Veda is a collection of poems or hymns composed in archaic Sanskrit by Indo-European-speaking peoples who lived in northwest India during the 2nd millennium BCE. 
      • There are four Vedas, the Rig Veda, Sama Veda, Yajur Veda and Atharva Veda. 
    • Rig Veda:
      • The Rigveda, or “Veda of Verses,” the earliest of those, is composed of about 1,000 hymns addressed to various deities and mostly arranged to serve the needs of the priestly families who were the custodians of that sacred literature.
    • Sama Veda:
      • The Samaveda, or “Veda of Chants,” is made up of a selection of verses—drawn almost wholly from the Rigveda—that are provided with musical notation and are intended as an aid to the performance of sacred songs.
    • Yajur Veda:
      • The Yajurveda, or “Veda of Sacrificial Formulas,” contains prose formulas applicable to various rites, along with verses intended for a similar purpose.
    • Atharva Veda:
      • It is a later compilation that includes incantations and magic spells.

    Source: IE