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Domino Chain Reaction

Domino Chain Reaction
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2024-11-06 03:11
VectorParametric EquationGeometric Construction
This GeoGebra example demonstrates the classic physical phenomenon of domino chain reaction, showcasing the principle of chain reaction. The involved mathematical concepts include vectors, parametric equations, and continuity. The construction uses GeoGebra commands such as Circle, CircleArc, Point, UnitVector, and Sequence to create the domino chain and the chain reaction animation. This example is suitable for middle school or high school students learning physics and mathematics related concepts.

GeoGebra Commands & Parameters

  1. Circle((0, 0), (r^(N - 1) * h)) → c
  2. CircleArc((0, 0), Rotate[(0, (r^(N - 1) * h)), (-angMax)], (0, (r^(N - 1) * h))) → arc
  3. Point(arc) → M
  4. UnitVector(Vector[Direction[Tangent[M, c]]]) → tanM
  5. Sequence(If[k > N - 1, Polygon[(w(r, k), 0), (w(r, k) - (a * r^(k)), 0), (w(r, k) - (a * r^(k)), (h * r^(k))), (w(r, k), (h * r^(k)))], Rotate[Polygon[(w(r, k), 0), (w(r, k) - (a * r^(k)), 0), (w(r, k) - (a * r^(k)), (h * r^(k))), (w(r, k), (h * r^(k)))], ang(N - k), (w(r, k), 0)]], k, 0, n - 1) → dom
  6. Sequence(Prism[Translate[dom(k), Vector[(0, 0, (((-an)) / 2 * r^(k - 1)))]], (an * r^(k - 1))], k, 1, n) → dom3D

AI Drawing Prompt Reference

Create a domino chain reaction style diagram: use the origin as the center to draw a circle and a circular arc based on radius and height power terms. Mark a point on the arc to serve as the first contact location. Determine the unit tangent direction at that point to guide the initial leaning direction. Then generate a sequence of multiple upright domino panels in 2D, placing each panel using parametric positions controlled by radius and height expressions, and rotating each successive panel by angle terms so the whole chain visually suggests a falling wave. Finally, extrude the 2D domino panels into 3D by converting them into prism-like blocks and translate them along the chain direction to form the 3D domino chain reaction look.
The prompt above was compiled from the original drawing commands and is for reference only.