Nested and Rotated Cubes by Steve Phelps

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2017-10-09 22:00

This example demonstrates the dynamic effects of nested and rotated cubes. It involves core mathematical concepts such as solid geometry, transformation, and sequences. The construction utilizes GeoGebra commands and objects like Point, Cube, and Sequence. Suitable for high school students and math enthusiasts to understand spatial geometry and transformations.

GeoGebra Commands & Parameters

Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
Sequence(Dilate[Rotate[Rotate[Rotate[a, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L
Sequence(Dilate[Rotate[Rotate[Rotate[A, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_1
Sequence(Dilate[Rotate[Rotate[Rotate[B, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_2
Sequence(Dilate[Rotate[Rotate[Rotate[C, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_3
Sequence(Dilate[Rotate[Rotate[Rotate[D, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_4
Sequence(Dilate[Rotate[Rotate[Rotate[E, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_5
Sequence(Dilate[Rotate[Rotate[Rotate[F, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_6
Sequence(Dilate[Rotate[Rotate[Rotate[G, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_7
Sequence(Dilate[Rotate[Rotate[Rotate[H, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_8