This animation solves a constrained optimization problem by turning algebra into geometry. Three right triangles with legs x, y, z and 4, 3, 1 are joined tip-to-tail so their vertical legs sum to 6 and horizontal legs sum to 8, aligning the hypotenuses into one straight line. The triangle inequality then shows the sum of square roots is minimized at 10, with the equality condition revealing the exact values of x, y, and z. Useful for students learning optimization through visual, non-calculus reasoning.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
Create a 25-second vertical 9:16 Instagram Reels math animation. SCENE 1: Display the problem: Given x + y + z = 6, find the minimum of √(x² + 16) + √(y² + 9) + √(z² + 1). SCENE 2: Draw three right triangles: Triangle 1: legs x and 4. Triangle 2: legs y and 3. Triangle 3: legs z and 1. Label their hypotenuses accurately. SCENE 3: Animate the three triangles joining tip-to-tail, with all corresponding sides aligned correctly. Show their vertical legs adding up to x+y+z=6 and horizontal legs adding up to 4+3+1=8. The hypotenuse segments must lie on one straight line, forming one large right triangle. SCENE 4: Show the calculation: Sum of hypotenuses ≥ √((x+y+z)² + (4+3+1)²) = √(6² + 8²) = 10. SCENE 5: Show equality when x:y:z = 4:3:1, giving x=3, y=9/4, z=3/4. Final answer: MINIMUM = 10. Clean white background, accurate geometry, smooth animation, readable mathematical labels, no people, no unnecessary effects. Keep the original mathematical expressions correct.