Pythagoras Theorem Visual Proof

Overview

A concise visual demonstration of the Pythagorean theorem, showing how the areas of the squares on the legs of a right‑angled triangle combine to equal the area of the square on the hypotenuse. The key takeaway is that for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship $a^{2}+b^{2}=c^{2}$ holds.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3s	Title "Pythagoras Theorem" fades in at the top, while a simple right‑angled triangle appears centered.
2	Construct Squares	~6s	Squares are drawn on each side of the triangle (on $a$, $b$, and $c$). The squares on the legs are colored blue, the square on the hypotenuse red.
3	Area Decomposition	~8s	The two blue squares are each split into a set of identical right‑triangle copies (four per square). These copies are animated to slide and re‑arrange inside the red square, perfectly filling it.
4	Equation Reveal	~4s	The algebraic statement $a^{2}+b^{2}=c^{2}$ appears at the bottom, highlighting each term as the corresponding area is shown.
5	Outro	~3s	All elements fade out, leaving only the final equation for a brief moment before the scene ends.

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Layout

┌───────────────────────────────────────┐
│               TOP AREA                 │
├───────────────────────┬───────────────┤
│                       │               │
│        LEFT AREA      │   RIGHT AREA  │
│   (main triangle &    │ (optional     │
│    squares)           │  supporting   │
│                       │  notes)       │
├───────────────────────┴───────────────┤
│               BOTTOM AREA              │
└───────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title "Pythagoras Theorem"	Fades in at start of Intro, stays through Phase 2, then fades out
Left	Central right‑triangle with its three attached squares; all animations of drawing, splitting, and sliding occur here	Primary visual focus
Right	Small caption "Right‑angled triangle" and optional legend for colors (blue = legs, red = hypotenuse)	Appears after Phase 2, stays until end
Bottom	Equation $a^{2}+b^{2}=c^{2}$ with term‑highlighting	Fades in during Phase 4, remains through Outro

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Notes

• Keep total runtime under 25 seconds to maintain brevity.
• Use smooth linear motions for the triangle copies moving between squares.
• Color palette: light blue for the two leg squares, soft red for the hypotenuse square, neutral gray for the triangle.
• No textual narration; visual cues (highlighting, fades) convey the logical steps.
• The scene must be implemented as a single Manim Scene class.