Dn Symmetry (Kaleidoscope)

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2017-11-16 01:58

In collections Playing With Symmetry

This example demonstrates Dn symmetry, creating symmetric patterns through rotation and mirroring operations. Key mathematical concepts include symmetry, transformations, and geometric construction. Using GeoGebra commands such as Rotate, Angle, Line, and Mirror, complex symmetric patterns can be constructed. Suitable for middle school students and teachers to understand the concepts of symmetry and transformations.

GeoGebra Commands & Parameters

Rotate(A, α, B) → A'
Angle(A, B, A') → β
Line(B, A) → f
Line(B, A') → g
Mirror(f, g) → f'
Mirror(g, f) → g'
Mirror(f, g') → f'_1
Mirror(g', f'_1) → g''
Mirror(g, f') → g'_1
Mirror(f', g'_1) → f''
Mirror(g'_1, f'') → h
Mirror(f'_1, g'') → i
Mirror(g'', i) → g'''
Mirror(i, g''') → i'
Mirror(f'', h) → f'''
Mirror(h, f''') → h'
Mirror(f''', h') → j
Mirror(h', j) → h''
Mirror(j, h'') → j'
Mirror(h'', j') → h'''
Mirror(j', h''') → j''
Mirror(C, g') → C'
Mirror(C, f) → C'_1
Mirror(C', f) → C''
Mirror(C, f') → C'_2
Mirror(C', f') → C''_1
Mirror(C'_1, f') → D
Mirror(C'', f') → C'''
Mirror(C, f''') → C'_3
Mirror(C', f''') → C''_2
Mirror(C'_1, f''') → E
Mirror(C'', f''') → C'''_1
Mirror(C'_2, f''') → F
Mirror(C''_1, f''') → G
Mirror(D, f''') → D'
Mirror(C''', f''') → H
Mirror(C, i) → C'_4
Mirror(C', i) → C''_3
Mirror(C'_1, i) → I
Mirror(C'', i) → C'''_2
Mirror(C'_2, i) → J
Mirror(C''_1, i) → K
Mirror(D, i) → D'_1
Mirror(C''', i) → L
Mirror(C'_3, i) → M
Mirror(C''_2, i) → N
Mirror(E, i) → E'
Mirror(C'''_1, i) → O
Mirror(F, i) → F'
Mirror(G, i) → G'
Mirror(D', i) → D''
Mirror(H, i) → H'
Mirror(C'_4, j'') → P
Mirror(C''_3, j'') → Q
Mirror(I, j'') → I'
Mirror(C'''_2, j'') → R