Cycloid Animation

Overview

A short vertical‑format animation showing the path traced by a fixed point on a rolling circle, revealing the cycloid curve. The viewer sees the wheel rolling, the red point leaving a yellow trail, and a concise explanation that the curve is called a cycloid.

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Phases

#	Phase Name	Duration	Description
1	Title & Intro	~3 s	Title "Bu noktanın yolu sence nasıl olur?" fades in from the top, subtitle "Çember dönerken kırmızı noktayı takip et!" appears below, then a short pause.
2	Ground Line	~1 s	A gray ground line is drawn across the bottom of the frame.
3	Wheel & Point Appear	~2 s	The blue wheel, white spoke, and red point appear together with a label "Noktanın izi çiziliyor..." at the bottom.
4	Rolling Motion	~8 s	The wheel rolls rightward while the red point traces a smooth yellow cycloid trail; the label remains visible.
5	Reveal Name	~2 s	The label fades out, then the text "Bu eğriye SİKLOİD denir." slides in from the bottom, followed by a brief description "Bir çember yuvarlanırken üzerindeki noktanın çizdiği yol."
6	Call‑to‑Action	~4 s	The description fades, the main text transforms into "Bunu biliyor muydun? Yorumlara yaz 👇", and the handle "@baranhocailematematik" appears near the bottom.
7	Outro Pause	~2 s	Final frame holds for a moment before ending.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │
│   Title & Subtitle (centered)               │
├───────────────────────┬─────────────────────┤
│                       │                     │
│      MAIN VISUAL      │   (empty – not used)│
│   (wheel, point, trail│                     │
│        & ground)      │                     │
├───────────────────────┴─────────────────────┤
│               BOTTOM AREA                  │
│   Labels / explanations / CTA (centered)   │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title and subtitle text, centered near the top edge.	Fade‑in at Phase 1, remain until Phase 2 ends.
Main Visual	Blue wheel, white spoke, red point, yellow trail, gray ground line.	Primary focus; wheel and point are always‑redrawn to follow the rolling motion.
Bottom	Dynamic label "Noktanın izi çiziliyor...", then cycloid name, short description, and final CTA with handle.	Text appears/fades according to phases; CTA transforms from previous text.

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Notes

• All animations are linear unless otherwise noted; the rolling motion uses a linear rate to keep the speed constant.
• The wheel radius, ground level, and start position follow the original parameters (radius ≈ 1.25, ground ≈ ‑3.2, start ≈ ‑4.2).
• The cycloid trail is drawn with a smooth VMobject that updates each frame, using about 120 points for visual smoothness.
• No additional text is shown beyond what is specified; all information is conveyed visually.
• The entire scene fits within a vertical 9 × 16 frame (portrait orientation) as in the original code.