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  • (a+b)2 = a2 + b2 + 2ab: This is how mathematics should be taught

    Anoop Kumar

    Member

    Updated: Oct 22, 2024
    Views: 1.5K
    Simplest explanation! Ever wondered why does this equation hold true? Check out the explanation -



    edit: typo mistake in heading, please correct to taught.
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  • Ramani Aswath

    MemberDec 8, 2012

    The Maharashtrian mathematecian Bhaskara II gave an interesting algebraic proof of the pythagorean Theorem:
    Proof #4
    [​IMG]
    The fourth approach starts with the same four triangles, except that, this time, they combine to form a square with the side (a + b) and a hole with the side c. We can compute the area of the big square in two ways. Thus
    (a + b)² = 4·ab/2 + c²
    simplifying which we get the needed identity.
    A proof which combines this with <a href="https://www.cut-the-knot.org/pythagoras/index.shtml#3" target="_blank" rel="nofollow noopener noreferrer">Pythagorean Theorem and its many proofs</a> is credited to the 12th century Hindu mathematician Bhaskara (Bhaskara II):
    [​IMG]
    Here we add the two identities
    c² = (a - b)² + 4·ab/2 and
    c² = (a + b)² - 4·ab/2
    which gives
    2c² = 2a² + 2b².
    The latter needs only be divided by 2.

    <a href="https://www.cut-the-knot.org/pythagoras/index.shtml" target="_blank" rel="nofollow noopener noreferrer">Pythagorean Theorem and its many proofs</a>

    TEachers must make it interesting to students.
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