Activity 2: The Incredible Shrinking Cube
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① This example dynamically demonstrates a cube shrinking and subdividing into smaller cubes, visualizing the recursive changes in area and volume. ② Core math concepts include cubes, geometric sequences, logarithmic functions, scaling of area and volume, and recursive division. ③ Construction highlights: using GeoGebra's Segment command to build edges and vertices (A to H and primed counterparts), with multiple segment objects (f, g, h, i, j, k, l, m, n, p, q, r, etc.) forming a 3D framework, and sliders or animations to control the scaling factor and observe the shrinking sequence. ④ Suitable for upper secondary or pre-university students, useful for exploring the connection between geometric scaling, sequences, and logarithmic functions, and as an interactive resource for math modeling or dynamic geometry lessons.
GeoGebra Commands & Parameters
Segment(A, B) → fSegment(A, D) → gSegment(A, H) → hSegment(B, E) → iSegment(E, F) → jSegment(E, H) → kSegment(F, G) → lSegment(D, G) → mSegment(H, G) → nSegment(B, C) → pSegment(C, F) → qSegment(C, D) → rSegment(A', D') → sSegment(A', H') → tSegment(A', B') → aSegment(B', E') → bSegment(E', F') → cSegment(E', H') → dSegment(D', G') → eSegment(F', G') → f_1Segment(H', G') → g_1Segment(B', C') → h_1Segment(C', F') → i_1Segment(C', D') → j_1Segment(A'', B'') → k_1Segment(A'', D'') → l_1Segment(A'', H'') → m_1Segment(B'', E'') → n_1Segment(E'', F'') → p_1Segment(E'', H'') → q_1Segment(D'', G'') → r_1Segment(F'', G'') → s_1Segment(G'', H'') → t_1Segment(B'', C'') → a_1Segment(C'', F'') → b_1Segment(C'', D'') → c_1