Differential Calculus Kaleidoscope

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2017-10-12 07:58

In collections Symmetry Explorations

This example demonstrates the construction of complex kaleidoscope patterns using transformations like rotation and reflection; core math concepts include differential calculus, function graphs, and geometric transformations; construction highlights: utilizes commands such as Line, Rotate, Angle, Mirror from GeoGebra, along with objects like α, A, B, a, β, b; suitable for high school and above students studying function transformations, geometric constructions, and applications of calculus.

GeoGebra Commands & Parameters

Line(A, B) → a
Rotate(B, α, A) → B'
Angle(B, A, B') → β
Line(A, B') → b
Mirror(a, b) → a'
Mirror(b, a') → b'
Mirror(a', b') → a''
Mirror(b', a'') → b''
Mirror(a'', b'') → a'''
Mirror(b'', a''') → b'''
Mirror(a''', b''') → c
Mirror(b''', c) → d
Mirror(c, d) → c'
Mirror(d, c') → d'
Mirror(c', d') → c''
Mirror(d', c'') → d''
Mirror(c'', d'') → c'''
Mirror(d'', c''') → d'''
Mirror(c''', d''') → e
Mirror(d''', e) → f
Mirror(C, b) → C'
Mirror(C', a') → C''
Mirror(C'', b') → C'''
Mirror(C''', a'') → D
Mirror(D, b'') → D'
Mirror(D', a''') → D''
Mirror(D'', b''') → D'''
Mirror(D''', c) → E
Mirror(C, d) → C'_1
Mirror(C', d) → C''_1
Mirror(C'', d) → C'''_1
Mirror(C''', d) → F
Mirror(D, d) → D'_1
Mirror(D', d) → D''_1
Mirror(D'', d) → D'''_1
Mirror(D''', d) → G
Mirror(E, d) → E'
Mirror(C, a) → C'_2
Mirror(C', a) → C''_2
Mirror(C'', a) → C'''_2
Mirror(C''', a) → H
Mirror(D, a) → D'_2
Mirror(D', a) → D''_2
Mirror(D'', a) → D'''_2
Mirror(D''', a) → I
Mirror(E, a) → E'_1
Mirror(C'_1, a) → J
Mirror(C''_1, a) → K
Mirror(C'''_1, a) → L
Mirror(F, a) → F'
Mirror(D'_1, a) → M
Mirror(D''_1, a) → N
Mirror(D'''_1, a) → O
Mirror(G, a) → G'
Mirror(E', a) → E''