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Perimeter vs Area

対象: Primary Schoolカテゴリ: Math

説明

A rectangle is shown on screen. The perimeter is demonstrated by a dot walking around all four sides while a counter adds up each side length. The area is then shown by filling the interior with a grid of unit squares, one column at a time. Both results are labeled with their standard formulas.

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Perimeter vs Area

Description

A rectangle is shown on screen. The perimeter is demonstrated by a dot walking around
all four sides while a counter adds up each side length. The area is then shown by
filling the interior with a grid of unit squares, one column at a time. Both results
are labeled with their standard formulas.

Phases

# Phase Name Duration Description
1 Title card 3 s Title "Perimeter vs Area" fades in
2 Rectangle intro 3 s Rectangle 5×3 drawn with side labels
3 Perimeter walk 10 s Dot travels along all 4 sides; counter shows running total
4 Perimeter formula 4 s Formula P = 2(l+w) = 2(5+3) = 16 shown
5 Clear & area intro 2 s Transition text "Now let's find the Area!"
6 Area fill 8 s 5×3 = 15 unit squares fill the interior one column at a time
7 Area formula 4 s Formula A = l×w = 5×3 = 15 shown
8 Both results 4 s Both P and A shown side-by-side; fade out

Layout

+--------------------------------------------------+
|            Perimeter vs Area                     |
|                                                  |
|        w = 3                                     |
|    +----------+      [counter: 0 → 16]           |
|  l=5|  (dot→) |                                  |
|    +----------+                                  |
|                                                  |
|   P = 2(l+w) = 16     A = l×w = 15              |
+--------------------------------------------------+

Area Descriptions

Area Content Notes
Top banner Title Large yellow text
Center Rectangle outline (5 units × 3 u) White stroke
Side labels "l = 5", "w = 3" White text next to sides
Walking dot Green dot moving around perimeter Smooth MoveAlongPath animation
Counter Running total, e.g. "+ 5 = 5" Cyan text top-right
Interior grid Unit squares filling the rectangle Blue fill, semi-transparent
Formula area P and A formulas Yellow MathTex

Assets & Dependencies

  • Fonts: LaTeX (MathTex), Manim default (Text)
  • Colors: YELLOW (title/formulas), GREEN (perimeter dot), CYAN (counter), BLUE (area fill)
  • Background: #1a1a2e
  • Manim version: ManimCE 0.19.1

Notes

  • Rectangle is 5 units wide × 3 units tall, scaled to fit nicely on screen.
  • Perimeter dot uses MoveAlongPath with a VMobject polygon path.
  • Unit squares for area use Square objects in a nested loop, faded in column by column.
  • Formula uses MathTex with highlight boxes around P and A.
Perimeter vs Area | AnimG | AnimG