Rotational Axis of a Cube

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2015-11-05 10:39

Vector Solid Geometry

This example demonstrates the geometric construction and properties of the rotational axis of a cube. It involves core mathematical concepts such as solid geometry, vectors, and rotational transformations. Key GeoGebra commands used include Cube, PointIn, Line, Rotate, and Midpoint. Suitable for high school geometry education to understand spatial geometric transformations.

GeoGebra Commands & Parameters

Cube(A, B, xOyPlane) → a, C, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, D, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH, E, F, G, H, faceABCD, faceADHE, faceABFE
PointIn(faceABCD) → J
PointIn(faceEFGH) → I
Line(I, J) → b
Rotate(a, (-α), b) → a'
Rotate(faceABCD, (-α), b) → faceABCD'
Rotate(faceABFE, (-α), b) → faceABFE'
Rotate(faceADHE, (-α), b) → faceADHE'
Rotate(faceBCGF, (-α), b) → faceBCGF'
Rotate(faceCDHG, (-α), b) → faceCDHG'
Rotate(faceEFGH, (-α), b) → faceEFGH'
Midpoint(F, H) → K
Midpoint(A, C) → L
Midpoint(F, C) → M
Midpoint(E, D) → N
Midpoint(H, C) → O
Midpoint(E, B) → P
Midpoint(edgeFG) → Q
Midpoint(edgeGH) → R
Midpoint(edgeEH) → S
Midpoint(edgeEF) → T
Midpoint(edgeBF) → U
Midpoint(edgeCG) → V
Midpoint(edgeBC) → W
Midpoint(edgeDH) → Z
Midpoint(edgeAE) → A_1
Midpoint(edgeAD) → B_1
Midpoint(edgeAB) → C_1
Midpoint(edgeCD) → D_1

AI Drawing Prompt Reference

Draw a cube and identify its rotational axis. Select a point on the bottom face and another on the top face of the cube, then connect these points to form a line, which represents the axis of rotation. Rotate the cube around this axis to observe the transformed shape. Additionally, calculate and mark the midpoints of all edges to better visualize the rotational effect.

The prompt above was compiled from the original drawing commands and is for reference only.