Proofs, the way they were first written.
We redraw classic proofs step by step — from Euclid's Elements to the Nine Chapters of ancient China — and tell their history with sources. Read them here, watch them on YouTube, and try them yourself.
Watch the full videos
Every proof from our Shorts, explained step by step with its history — 4 to 6 minutes each.
-
Heron's Formula: How to Find a Triangle's Area from Its Three Sides · 3:11
-
Why Tall Columns Buckle: From Roman Temples to New York Skyscrapers · 4:20
-
How Big Is the Earth? Eratosthenes, al-Ma'mun and al-Biruni's Hill · 3:48
-
The Chickens and Rabbits Puzzle: From Ancient China to Computer Proofs · 3:51
-
The Seven Bridges of Königsberg: How Euler Proved the Walk Impossible · 3:34
-
Pascal's Triangle Before Pascal: India, Persia, China and Europe · 3:37
-
Aryabhata's Pi: the 1,500-Year-Old Verse, Read Line by Line · 4:14
-
Volume of a Sphere: How Archimedes Found It — and Wanted It on His Tomb · 3:41
-
Gaussian Elimination Long Before Gauss — The Nine Chapters · 3:57
-
The Golden Ratio, the Way Euclid Built It — and the Myths that Came Later · 4:51
-
The Rules of Zero: what Brahmagupta wrote in 628, and the one he got wrong · 4:13
-
Completing the Square, the Way al-Khwarizmi Did It — algebra without symbols · 4:19
-
Garfield's Proof of the Pythagorean Theorem — the congressman's trapezoid, step by step · 4:16
-
The Fibonacci Sequence Was Known Before Fibonacci — Thanks to Poetry · 4:47
-
Euclid's Proof of the Pythagorean Theorem — step by step, as he wrote it · 5:49
The video loads from YouTube (youtube-nocookie.com) only after you click. See our privacy policy. All videos on YouTube
Every page here follows the same three steps: a clear explanation in today's words, the original method as it appears in the oldest surviving sources, and something to try yourself. Legends are marked as legends, and modern illustrations are marked as modern.