Slow Reveal of n-Dimensional Sphere Volume Formula

Scene Overview

• A single Manim Scene that displays the formula for the volume of an n‑dimensional sphere using a slow typewriter effect.
• Background color: solid vibrant green (#00FF00).
• Formula color: bold black.
• The formula is centered on the screen.
• Total duration of the typewriter animation: at least 5 seconds (approximately 6 seconds to ensure a very slow reveal).

Mathematical Content

• Formula (LaTeX):
  V_{n}(R) = \frac{\pi^{n/2}}{\Gamma\left(\frac{n}{2} + 1\r\right)} R^{n}

Visual Elements

• Background: BackgroundRectangle or scene background set to #00FF00.
• Text object: MathTex containing the formula, with color=BLACK and font_weight='bold'.
• The MathTex object is positioned at the origin (center of the screen).

Animation Timing & Transitions

• Use the Write animation (or equivalent AddTextLetterByLetter style) on the MathTex object.
• Set run_time to 6 seconds to achieve a very slow typewriter effect.
• Ensure the animation reveals the formula letter‑by‑letter in natural reading order.
• No additional transitions before or after; the scene ends with the fully displayed formula.

Camera & Perspective

• Default camera; no zoom or pan needed since the formula is centered and fully visible.

Additional Details

• No extra text or labels are used.
• The scene contains exactly one Scene class.
• All visual styling respects the requirement for bold black text on a vibrant green background.