Exploring Nature's Symmetry

Loading the math board and drawing, please wait…

2017-03-02 21:00

Probability & Statistics Transformation Geometric Construction

This is an activity example exploring symmetry in nature. Using GeoGebra, we can observe and understand the symmetry in nature. The core mathematical concepts involved include geometric transformations and symmetry. By using commands such as Point, Mirror, and Polygon, we can construct symmetric shapes. Suitable for middle school students to understand the beauty of symmetry in nature.

GeoGebra Commands & Parameters

Point(xAxis) → A
Point(a) → H
Mirror(C, a) → C'_1
Mirror(D, a) → D'_1
Mirror(E, a) → E'_1
Mirror(F, a) → F'_1
Mirror(G, a) → G'_1
Mirror(H, a) → H'_1
Polygon(B, C, D'_1, C'_1, D, E, F, G, H, G'_1, F'_1, E'_1) → poly1, b, e', d', c', c, d, e, f, g, h, g', f'
Mirror(B, i) → B'
Mirror(C, i) → C'
Mirror(D, i) → D'
Mirror(E, i) → E'
Mirror(F, i) → F'
Mirror(G, i) → G'
Mirror(H, i) → H'
Mirror(G'_1, i) → I
Mirror(F'_1, i) → J
Mirror(E'_1, i) → K
Mirror(D'_1, i) → L
Mirror(C'_1, i) → M
Polygon(B', C', L, M, D', E', F', G', H', I, J, K) → poly1', b', k, l, m, c'_1, d'_1, e'_1, f'_1, g'_1, h', i_1, j_1
Mirror(B', j) → B''
Mirror(C', j) → C''
Mirror(D', j) → D''
Mirror(E', j) → E''
Mirror(F', j) → F''
Mirror(G', j) → G''
Mirror(H', j) → H''
Mirror(I, j) → I'
Mirror(J, j) → J'
Mirror(K, j) → K'
Mirror(L, j) → L'
Mirror(M, j) → M'
Polygon(B'', C'', L', M', D'', E'', F'', G'', H'', I', J', K') → poly1'', b'', k', l', m', c'', d'', e'', f'', g'', h'', i', j'
Mirror(B'', i) → B'''
Mirror(C'', i) → C'''
Mirror(D'', i) → D'''
Mirror(E'', i) → E'''
Mirror(F'', i) → F'''
Mirror(G'', i) → G'''
Mirror(H'', i) → H'''
Mirror(I', i) → I''
Mirror(J', i) → J''
Mirror(K', i) → K''
Mirror(L', i) → L''
Mirror(M', i) → M''
Polygon(B''', C''', L'', M'', D''', E''', F''', G''', H''', I'', J'', K'') → poly1''', b''', k'', l'', m'', c''', d''', e''', f''', g''', h''', i'', j''