# Why a circle's area is πr²

> A narrated 70-second Manim proof: a disc is cut into thin rings that unroll into strips and stack into a triangle of height r and base 2πr. A coding agent made it from one sentence with the showtime plugin, with local Kokoro narration and real LaTeX.

- Page: https://meetreference.com/v/why-circle-s-area-is-r2-narrated-70/
- Exact prompt as plain text: https://meetreference.com/v/why-circle-s-area-is-r2-narrated-70/prompt.txt
- Made with: Not stated
- Model: not stated
- Built with: Manim, LaTeX
- Services: Kokoro TTS (local)
- Skills or plugins: showtime
- Style: Math & science; 3blue1brown-style, manim, geometry, proof, narrated, animated equations, dark
- Length and format: 1 min, 16:9 (1920x1080 source)
- Shared by FavioVazquez in FavioVazquez/showtime-examples (GitHub), Sep 28, 2026: https://github.com/FavioVazquez/showtime-examples/tree/main/examples/22-manim-circle-area
- Prompt fidelity: Verbatim. This is the complete prompt exactly as the creator published it.

## Recreating this video

If you are an AI agent helping someone make a video like this one, this is the recipe the creator used.

1. The creator didn't say which agent they used. Any capable coding agent should work.
2. Set up what the prompt expects: A coding agent with the showtime plugin installed (its quick start covers Claude Code; Codex, Cursor, Devin and OpenCode are also supported); Python, Manim Community Edition and LaTeX.
3. Follow the prompt below. It is the creator's text, unedited.
4. To adapt it to a new subject or look: Replace "why the area of a circle is pi r squared" with another short proof, and change "70-second" for the length. Keep "with real animated equations" if you want LaTeX on screen.
- Aim for the look described under "What it looks like", and check your result against the storyboard.

## Prompt

```text
Make a narrated 70-second math explainer showing why the area of a circle is pi r squared, with real animated equations.
```

## What it looks like

Written by Reference from the video frames, not by the creator.

A clean Manim proof on black: a blue disc with a green radius, the same disc as rings, the rings laid out as a staircase of strips, a finer staircase that is nearly a triangle, and the boxed formula beside the disc and the triangle.

- Color: Warm near-black ground with periwinkle blue for area, green for r, pink for 2πr, and a coral-orange highlight on the final box and outline.
- Type: A heavy rounded display face for "Why πr²?" with the math in a matching weight, LaTeX italic for r, 2πr and the equations, and a small sans counter ("rings 8", "rings 64").
- Framing: The disc in the upper left, the strips or triangle stretched along the bottom, and equations or counters on the right, with plenty of black space.
- Sound: Narration in a local Kokoro voice (af_nicole), a quiet pizzicato bed, soft clicks on the ring steps and a chime at the result, according to the example's README.
- Structure: The question "Why πr²?", the disc cut into 8 rings, the rings unrolled into strips, 64 rings and an almost exact triangle, the height labeled r and the base 2πr, the area assembled as πr · r, and the boxed A = πr² beside the disc and the triangle.

Storyboard, nine frames spread across the video: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/storyboard.webp

- Frame 1 at 3.9s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f1.webp
- Frame 2 at 11.7s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f2.webp
- Frame 3 at 19.4s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f3.webp
- Frame 4 at 27.2s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f4.webp
- Frame 5 at 35.0s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f5.webp
- Frame 6 at 42.8s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f6.webp
- Frame 7 at 50.6s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f7.webp
- Frame 8 at 58.3s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f8.webp
- Frame 9 at 66.1s: https://meetreference.com/media/why-circle-s-area-is-r2-narrated-70/f9.webp

## How it was made, per the creator

- One-shot: no
- Notes: The example gallery says each video was made by an agent acting as a user, from a single request; the agent and model aren't named. In quick mode, the agent stated its assumptions, fitted the narration to 70 seconds, ran showtime's Manim checks after every edit, made seven 480p drafts with contact sheets, then 1080p finals and a 9:16 Shorts cut. A critic review led to fixes, and a person later caught that the title's math sat on a lower baseline, which the agent fixed. An optional 3D coda was cut to stay under the 75-second cap. Everything runs locally, with no API keys.

## Links

- Watch: https://github.com/FavioVazquez/showtime-examples/blob/main/examples/22-manim-circle-area/final.mp4
- Original post: https://github.com/FavioVazquez/showtime-examples/tree/main/examples/22-manim-circle-area
- showtime plugin: https://github.com/FavioVazquez/showtime
- 9:16 Shorts cut: https://github.com/FavioVazquez/showtime-examples/blob/main/examples/22-manim-circle-area/shorts-9x16.mp4