Snowflakes and Kaleidoscopes

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2017-11-22 00:49

In collections Playing With Symmetry

This GeoGebra example showcases the beauty of snowflakes and Kaleidoscope patterns through transformations and reflections. It involves key mathematical concepts such as vectors, reflections, and transformations. Using commands like Rotate, Angle, Line, and Mirror, users can create complex geometric patterns. Suitable for high school and above students or teachers for teaching and exploring geometric transformations.

GeoGebra Commands & Parameters

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