The Pythagorean Theorem : Two Proofs
patrickJMT・2 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.
