Garfield's proof of the Pythagorean theorem | Geometry | Khan Academy

TL;DR

James Garfield, the 20th US President, discovered a proof of the Pythagorean theorem while serving as a member of the US House of Representatives.

Transcript

What we're going to do in this video is study a proof of the Pythagorean theorem that was first discovered, or as far as we know first discovered, by James Garfield in 1876, and what's exciting about this is he was not a professional mathematician. You might know James Garfield as the 20th president of the United States. He was elected president. H... Read More

Key Insights

• ❓ James Garfield discovered a proof of the Pythagorean theorem, showcasing his interest and knowledge in geometry.
• 🔺 The proof involves constructing two congruent triangles within a right triangle to analyze the angles.
• 🔺 By understanding the angle relationships, Garfield establishes that the mystery angle within the right triangle is 90 degrees.

Questions & Answers

Q: How did James Garfield prove the Pythagorean theorem?

Garfield constructed a right triangle and used it to create a congruent triangle. By comparing the angles of both triangles, he showed that the mystery angle within the right triangle is 90 degrees, proving the theorem.

Q: Was James Garfield a professional mathematician?

No, James Garfield was not a professional mathematician. He was the 20th US President and discovered the proof while serving in the US House of Representatives.

Q: What are the lengths of the sides of the right triangle constructed by James Garfield?

Garfield's right triangle had sides of length a, b, and c, where a and b are the shorter sides and c is the hypotenuse.

Q: How did Garfield use the trapezoid to calculate the area?

Garfield considered the trapezoid as the sum of its component parts - two right triangles and a large triangle. By calculating the areas of these individual parts, he arrived at the same result as the area formula for a trapezoid.

Summary & Key Takeaways

• James Garfield, the 20th US President, discovered a proof of the Pythagorean theorem while serving as a member of the US House of Representatives.

• Garfield constructed a right triangle and then used it to construct another congruent triangle to prove the theorem.

• By analyzing the angles of both triangles, Garfield showed that the mystery angle within the right triangle is 90 degrees.