Pythagorean Theorem – Rotating Shapes

Overview

A 2‑minute visual exploration of the Pythagorean theorem using rotating squares on the sides of a right‑angled triangle. The animation builds step‑by‑step, showing how the areas of the two smaller squares combine to equal the area of the largest square, while the formula $a^2 + b^2 = c^2$ appears at the end. An additional short example illustrating the theorem with concrete numeric lengths is included after the main proof.

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Phases

#	Phase Name	Duration	Description
1	Intro	~8 s	Title fades in, a right‑angled triangle appears centered, with side labels $a$, $b$, $c$.
2	Build Squares	~18 s	Squares are constructed on each side of the triangle, each growing from the side outward.
3	Rotate & Align	~35 s	The two smaller squares rotate around the triangle, aligning their areas over the large square in a smooth, creative motion.
4	Step‑by‑Step Proof	~30 s	On the right side, a concise three‑step visual proof is displayed: (1) area of square on $a$, (2) area of square on $b$, (3) combined area equals area of square on $c$.
5	Numeric Example	~20 s	A concrete example (e.g., $a=3$, $b=4$, $c=5$) is shown: the squares are filled with a grid, the areas are counted, and the equality $9+16=25$ is highlighted.
6	Outro	~9 s	The formula $a^2 + b^2 = c^2$ appears centered, all elements fade out.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │
├──────────────────────┬──────────────────────┤
│                      │                      │
│      LEFT AREA       │     RIGHT AREA       │
│  (triangle & squares)│ (proof steps)        │
│                      │                      │
├──────────────────────┴──────────────────────┤
│                 BOTTOM AREA                 │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title "Pythagorean Theorem" (large, bold)	Fades in during Intro, stays until Outro
Left	Central right‑angled triangle with three rotating squares; later the numeric example squares appear with grid shading	Primary visual focus; squares grow, rotate, and later display the example
Right	Three numbered visual steps, each with a small diagram and brief label (e.g., "Area $a^2$")	Appears at start of Phase 4, stays through Phase 5
Bottom	Small caption "© YourName – 2026"	Fades in with Outro

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Notes

• All rotations are smooth 360° arcs; the two smaller squares each rotate 90° to line up with the large square’s interior.
• Colors: distinct but harmonious (e.g., blue for $a$, orange for $b$, green for $c$).
• The numeric example uses a light grid pattern inside each square to make the counted unit squares visible.
• No spoken narration; visual cues and brief on‑screen labels convey the steps.
• Total runtime is now ~120 seconds to meet the 2‑minute request while keeping each phase clear.
• Downloading the video: Render the scene with Manim using a command such as manim -pql your_script.py PythagoreanTheoremScene. The exported video will be saved in the media/videos/ directory (e.g., media/videos/your_script/480p15/YourSceneName.mp4). After rendering, the file can be copied or downloaded from that location. If using an online IDE or cloud service, locate the media folder in the file explorer and download the .mp4 file directly.