Chain Reaction Effect
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This is a GeoGebra example that demonstrates a simple chain reaction effect of domino. The example involves core mathematical concepts in geometry and statistics, particularly the statistical concepts of standard deviation and mean. The example uses GeoGebra commands and objects, including Circle, CircleArc, Point, UnitVector, Sequence, etc. The example is suitable for middle school or high school students learning statistics and geometry concepts.
GeoGebra Commands & Parameters
Circle((0, 0), (r^(N - 1) * h)) → cCircleArc((0, 0), Rotate[(0, (r^(N - 1) * h)), (-angMax)], (0, (r^(N - 1) * h))) → arcPoint(arc) → MUnitVector(Vector[Direction[Tangent[M, c]]]) → tanMSequence(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) → domSequence(Prism[Translate[dom(k), Vector[(0, 0, (((-an)) / 2 * r^(k - 1)))]], (an * r^(k - 1))], k, 1, n) → dom3D
AI Drawing Prompt Reference
Draw a 2D circle centered at the origin with radius given by a power of r times h, then construct a circular arc on that circle. Choose a point on the arc to serve as the reference for the tangent direction, and determine the unit tangent vector at that point. Next, generate a sequence of domino-like quadrilateral blocks parametrically for k from 0 to n−1, using a base width defined by w(r,k) and a shifted bottom edge computed with a·r^k; the blocks extend upward to height h·r^k, and each block is rotated progressively around its bottom endpoint according to ang(N−k). Finally, lift the whole 2D chain into 3D by turning each block into a prism and translating it along the z direction with a k-dependent offset, forming a 3D chain-reaction domino effect.
The prompt above was compiled from the original drawing commands and is for reference only.