Cube Mirror Transformation Animation
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Similarity, Right Triangles, and Trigonometry (SRT) Cluster
This example demonstrates the mirror transformation of a cube in 3D space. Key mathematical concepts include mirror transformations in solid geometry and geometric construction. Using GeoGebra commands such as Mirror, Intersect, and Dilate, a mirror transformation animation of the cube is constructed. Suitable for high school or university solid geometry courses.
GeoGebra Commands & Parameters
Mirror(G, f) → G'Mirror(F, f) → F'Mirror(E, g) → E'Mirror(F, g) → F'_1Mirror(G, g) → G'_1Mirror(F', g) → F''Mirror(G', g) → G''Mirror(E, f) → E'_1Mirror(E'_1, g) → HIntersect(g, j) → IIntersect(g, i) → JIntersect(g, h) → KDilate(L, If[0 < a ≤ 1, 1 - a, 0], J) → L'Segment(L, L') → kDilate(J, If[1 < a ≤ 2, 2 - a, 0], F) → K'Polygon(L, J, F) → poly1, n, e, k_1Dilate(F, If[2 < a ≤ 3, 3 - a, 0], L) → E'_2Rotate(K, If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K'_1Rotate(K', If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K''Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_1Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_2Rotate(E, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → E'_3Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_3Rotate(K', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K''_1Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_2Rotate(L', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L''Rotate(K'', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'''_1Rotate(L'_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → QRotate(K'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → RRotate(E'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → SRotate(K'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → TRotate(K''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → URotate(L'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → VRotate(L'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → L'''Rotate(K'''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → WRotate(Q, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Q'Rotate(R, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → R'Rotate(S, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → S'Rotate(V, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → V'Rotate(L''', If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → ZRotate(W, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → W'Rotate(T, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → T'Rotate(U, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → U'Rotate(K'_1, If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → E_1Rotate(K'', If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → K'''_2Dilate(K, If[9 < a ≤ 10, 10 - a, 0], E') → K'_4Rotate(E_1, π / 2, L) → T_1Rotate(K'''_2, π / 2, L) → U_1Rotate(K'''_2, π, L) → W_1Rotate(E_1, (3 * π / 2), L) → Z_1Rotate(K'''_2, (3 * π / 2), L) → A_2Segment(J, K') → lSegment(F, E'_2) → mRotate(L, If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L'_3Rotate(L', If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L''_1Segment(L'_3, L''_1) → k'_1Circle(L, 0.5) → d_1Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_4Rotate(J, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → J'Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_2Polygon(L'_4, J', F'_2) → poly1'_1, f'_2, l'_4, j'Rotate(L'_3, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → MRotate(L''_1, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → NSegment(M, N) → bRotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_5Rotate(L', If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L''_2Segment(L'_5, L''_2) → k'_3Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_3Rotate(E'_2, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → PSegment(F'_3, P) → m'Rotate(L'_4, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → ORotate(J', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → J''Rotate(F'_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → F_1Polygon(O, J'', F_1) → poly3, f_2, o, j''Rotate(M, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → M'Rotate(N, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → N'Segment(M', N') → b'Rotate(L'_5, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → G_1Rotate(L''_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → H_1Segment(G_1, H_1) → pRotate(F'_3, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → I_1Rotate(P, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → P'Segment(I_1, P') → m''Rotate(O, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → O'Rotate(J'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J'''Rotate(F_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J_1Polygon(O', J''', J_1) → poly3', j_2, o', j'''Rotate(M', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → M''Rotate(N', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → N''Segment(M'', N'') → b''Rotate(G_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q_1Rotate(H_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R_1Segment(Q_1, R_1) → p'Rotate(I_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S_1Rotate(P', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → P''Segment(S_1, P'') → m'''Intersect(d_1, x = 0) → B_2, C_2Line(L, F) → qIntersect(d_1, q) → D_2, E_2CircleSector(L, E_2, B_2) → rRotate(r, If[9 < a < 10, ((-(a - 9)) * π / 4), ((-π)) / 4], L) → r'Segment(L''_2, B) → sSegment(L', A) → tSegment(D, N'') → f_1Segment(H_1, C) → g_1
AI Drawing Prompt Reference
Draw a cube in 3D space and animate its mirror transformations across two planes. Start with the original cube, then create mirrored copies about each plane. Use a slider to sequentially show rotations, dilations, and mirroring of the cube and its parts, including vertices, edges, and faces. The scene includes multiple cubes, their mirrors, and auxiliary planes and intersection points, demonstrating symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.