Animate a Pythagorean Theorem Proof | QuantumSketch
Animate the Pythagorean theorem with the rearrangement proof: squares on the legs slide and recombine into the square on the hypotenuse, showing a²+b²=c².
Animate the Pythagorean theorem with the rearrangement proof: draw a square on each side of a right triangle, then slide and rotate the two smaller squares' pieces until they exactly fill the largest square. Conserved area proves a² + b² = c² with no algebra.
The theorem on screen
For a right triangle with legs a, b and hypotenuse c. The squares-on-sides picture turns this into a statement about areas.
The rearrangement proof, beat by beat
- Draw the right triangle with legs a, b.
- Build a square on each side — areas a², b², c².
- Pose the question: do the two small squares fill the big one?
- Cut and slide — pieces of the a² and b² squares translate/rotate into the c² square.
- They fit perfectly — no gaps, no overlap → a² + b² = c².
Because nothing is added or removed, area is conserved, and the equality is seen, not computed.
Why visual proofs land
| Approach | Student reaction | |---|---| | Algebraic proof | "I followed the steps" | | Rearrangement animation | "Oh — it has to be true" |
Watching area physically move is more convincing than symbol manipulation.
Manim building blocks
Polygon and Square for the shapes, Transform/Rotate to slide pieces, and MathTex to label a², b², c². Areas stay exact because Manim computes coordinates, not pixels — see Why Manim Beats Generative Video.
The prompt
"Draw a 3-4-5 right triangle with a square on each side, then rearrange the two smaller squares' pieces to fill the square on the hypotenuse, proving a² + b² = c²."
→ Render it at quantumsketch.app.
Written by Shihab Shahriar Antor · Shahriar Labs
FAQ
Q.What's the best visual proof of the Pythagorean theorem to animate?
The rearrangement proof is the most satisfying to animate. Start with a right triangle and draw a square on each of its three sides. The claim a² + b² = c² becomes 'the two smaller squares have the same total area as the big one.' You then animate the smaller squares being cut into pieces that slide and rotate to exactly fill the square on the hypotenuse, with no gaps or overlaps. Because area is visibly conserved during the rearrangement, the equality is proven without algebra — viewers see the two areas literally become one.
Q.How do I animate a geometry proof without drawing software?
Describe the proof as a prompt: 'Draw a right triangle with squares on each side, then rearrange the two smaller squares' pieces to fill the square on the hypotenuse, proving a² + b² = c².' QuantumSketch turns it into a narrated Manim animation. Manim's Polygon, Square, and Transform objects handle the cutting, sliding, and rotating of pieces precisely, so areas are conserved exactly. You choose the triangle and the proof style; the tool renders the geometry.