November 29, 2025
Lasagna vs geometry showdown
Garfield's Proof of the Pythagorean Theorem
Yes, a U.S. president proved the triangle rule—and the comments are pure chaos
TLDR: A U.S. president, James A. Garfield, published a clever proof of the triangle rule in 1876. Commenters split between admiration and memes, debating Pythagoras’s credit, comparing proofs, and demanding lasagna jokes—proving math history can spark big feelings and bigger punchlines.
Move over cartoon cat: the original Garfield—James A. Garfield, America’s 20th president—dropped a clever proof of the triangle rule back in 1876. Using the area of a trapezoid (a four‑sided shape with one set of parallel sides), he showed the simple relationship behind right triangles. History buffs note he’s the only U.S. president to add something original to math, and the crowd is split between awe and memes.
And the comments? Wunderlust lit the match with “American presidents used to be smart,” while b800h confessed they were “ready for it to involve lasagna,” igniting a flood of Garfield-the-cat jokes. vee-kay stirred controversy, arguing Pythagoras may not have written the theorem at all, and that the credit came centuries later. Meanwhile WCSTombs hyped a favorite proof “attributed to Einstein,” and einpoklum insisted Garfield’s trick looks like “half” of the classic square rearrangement, dropping a handy visual.
The thread became a showdown: Team Triangles vs Team Squares vs Team Lasagna. Some hail Garfield as a forgotten math hero; others say the real drama is who gets credit—Pythagoras, presidents, or students finding new proofs today. A brainy president proving geometry makes for delicious internet drama.
Key Points
- •James A. Garfield published an original Pythagorean theorem proof on April 1, 1876, in the New-England Journal of Education.
- •Garfield was a congressman from Ohio at the time and later became the 20th U.S. president, serving from March 4, 1881, until his death on September 19, 1881.
- •The proof uses a geometric construction with points B, D, and E to form a trapezoid ACED and congruent triangles ABC and BDE.
- •The trapezoid’s area is computed both as height × average of parallel sides and as the sum of three triangle areas.
- •Equating the two area expressions and simplifying yields a² + b² = c², proving the Pythagorean theorem.