A Derivative Explained Through Moving Diagrams
A six-minute Mandarin calculus lesson that turns a moving car into a graph, a limiting secant, a derivative formula, and a final magnified intuition.
Field notes / why it works
The opening question appears with a gold title by 0:02.75, giving the abstract topic an immediate puzzle. A single example changes form from car to number line to graph, then four shrinking intervals at 1:37–2:14 make the limit visible before its formula appears at 2:37. The worked proof at 3:17–4:01 confirms the earlier result, and the curve magnification at 5:34–6:00 closes with a visual payoff.
Plate 01 / The format in one breath
A calm, continuous mathematical animation takes an everyday puzzle and makes it measurable. One small example becomes a graph; the graph becomes a formal rule; the rule becomes an application and a final visual intuition. The narration is continuous, while diagrams draw and transform on a near black canvas.
Why it works
- The first 2.75 seconds write a gold concept title over a question; the narration opens with the same puzzle, so the promise is clear before any example.
- From 0:36 to 2:22, a car, a number line, a curve, a secant and a tangent express one idea at increasing levels of abstraction. Each step preserves the previous one.
- The derivation at 3:19–3:50 resolves the earlier numerical result, and 5:27–5:56 pays it off with a magnified curve that looks straight nearby.
Plate 02 / Format card
| Reference | |
|---|---|
| Platform · aspect · length | X · 16:9 · 6:00.1 · 1280 × 720 · 30 fps |
| Pace | 1 continuous rendered shot; 0 camera cuts/min; 11 detected major internal changes, about 1.8/min. Graph and label motion occurs within these long states. |
| Script | Mandarin Chinese; 1,131 Whisper word units, 189 units/min overall. Chinese word segmentation makes this an approximate pace proxy. Five detected questions; 44 number mentions. |
| Voice | High register, animated but instructional synthetic sounding narrator (inferred from post's edge-tts credit). No visible presenter. |
| On screen | 100% vector motion graphics: typography, simple object icon, number line, axes, curves, formulas, callouts. |
| Captions | Full sentence white subtitles in a near black bottom strip, usually one line; separate large labels and equations within the diagram. |
| Sound | Dry narration, no detectable music bed; −19.7 LUFS integrated, −5.5 dBFS true peak. |
| Structure | 8 teaching beats; numerical reveal around 2:14, algebraic proof around 3:49, visual payoff at 5:38; no CTA. |
Pro / 13 plates + recipe
The first plates are open. The full dissection is Pro.
Get the timed shots, type and sound specs, and the runnable recipe.
Open the full blueprint- Plate 03 / The hook, frame by frame (first 3 seconds)Pro
- Plate 04 / Structure (beat sheet)Pro
- Plate 05 / Shot grammarPro
- Plate 06 / Visual style guidePro
- Plate 07 / Voice and deliveryPro
- Plate 08 / Sound designPro
- Plate 09 / PackagingPro
- Plate 10 / Script templatePro
- Plate 11 / Production planPro
- Plate 12 / PromptsPro
- Plate 13 / Edit recipePro
- Plate 14 / QA checklistPro
- Plate 15 / Make it yoursPro
- Recipe / runnable promptPro