The Pythagorean Theorem : Two Proofs

patrickJMT2 minutes read

The video discusses two proofs for the Pythagorean theorem, with the second attributed to former President Garfield, highlighting the fundamental concept that a^2 + b^2 = c^2. Both proofs involve geometric shapes like squares, triangles, and trapezoids to derive the theorem.

Insights

  • President Garfield's proof of the Pythagorean theorem involves utilizing a trapezoid formed by two triangles, offering a unique perspective on a well-known mathematical concept.
  • Both proofs ultimately lead to the same conclusion: a^2 + b^2 = c^2, emphasizing the universality and significance of the Pythagorean theorem in mathematics.

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Recent questions

  • What is the Pythagorean theorem?

    A^2 + b^2 = c^2

  • How many proofs are discussed for the Pythagorean theorem?

    Two

  • Who is attributed with the second proof of the Pythagorean theorem?

    President Garfield

  • What is the formula for the area of a trapezoid?

    1/2 x (sum of bases) x height

  • Why is the Pythagorean theorem considered fundamental?

    Likely known by most people if mentioned

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Summary

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Pythagorean Theorem: Two Proofs Explored

  • Two proofs for the Pythagorean theorem are discussed in the video, with the second attributed to former President Garfield.
  • The Pythagorean theorem is highlighted as a fundamental concept, likely known by most people if mentioned.
  • The first proof involves creating a square with four triangles inside, calculating their areas to derive the theorem.
  • The second proof by President Garfield involves forming a trapezoid from two triangles, leading to the same theorem.
  • The area of a trapezoid is explained as 1/2 times the sum of the bases multiplied by the height.
  • By simplifying the equations derived from the trapezoid and triangle areas, both proofs conclude with a^2 + b^2 = c^2, where c represents the hypotenuse.
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