String Art Symmetry & Translations
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This example demonstrates string art symmetry and translations. It involves key concepts such as symmetry and translation. Using GeoGebra commands like Sequence, Segment, Mirror, and Translate, complex geometric shapes can be constructed. Suitable for middle school students learning geometric transformations.
GeoGebra Commands & Parameters
Sequence((i / a * A) + ((a - i) / a * D), i, 0, a) → L_2Sequence((i / a * B) + ((a - i) / a * A), i, 0, a) → L_1Segment(D, A) → gSequence(Segment[Element[L_1, i], Element[L_2, i]], i, 1, a + 1) → L_3Mirror(L_2, yAxis) → L_4Mirror(L_1, yAxis) → L_5Mirror(L_3, yAxis) → L_6Mirror(D, yAxis) → D'Mirror(A, yAxis) → A'Segment(D', A') → g'Mirror(B, yAxis) → B'Mirror(L_3, xAxis) → L_7Mirror(D, xAxis) → D'_1Mirror(A, xAxis) → A'_1Segment(D'_1, A'_1) → g'_1Mirror(D', xAxis) → D''Mirror(A', xAxis) → A''Segment(D'', A'') → g''Mirror(B, xAxis) → B'_1Mirror(L_1, yAxis) → L_8Mirror(L_7, yAxis) → L_9Mirror(D'_1, yAxis) → CMirror(A'_1, yAxis) → ESegment(C, E) → hMirror(D'', yAxis) → D'''Mirror(A'', yAxis) → A'''Segment(D''', A''') → g'''Mirror(A, yAxis) → A'_2Mirror(B, yAxis) → B'_2Mirror(A', yAxis) → A''_1Mirror(B'_1, yAxis) → FVector(G, H) → uVector(G, I) → vTranslate(L_2, u) → L_{10}Translate(L_1, u) → L_{11}Translate(L_3, u) → L_{12}Translate(L_4, u) → L_{13}Translate(L_5, u) → L_{14}Translate(L_6, u) → L_{15}Translate(L_7, u) → L_{16}Translate(L_8, u) → L_{17}Translate(L_9, u) → L_{18}Translate(D, u) → D'_2Translate(A, u) → A'_3Segment(D'_2, A'_3) → g'_2Translate(D', u) → D''_1Translate(A', u) → A''_2Segment(D''_1, A''_2) → g''_1Translate(D'_1, u) → JTranslate(A'_1, u) → KSegment(J, K) → iTranslate(D'', u) → D'''_1Translate(A'', u) → A'''_1Segment(D'''_1, A'''_1) → g'''_1Translate(C, u) → C'Translate(E, u) → E'Segment(C', E') → h'Translate(D''', u) → LTranslate(A''', u) → MSegment(L, M) → jTranslate(v, u) → v'Translate(B, u) → B'_3Translate(B', u) → B''Translate(B'_1, u) → NTranslate(A'_2, u) → OTranslate(B'_2, u) → PTranslate(A''_1, u) → QTranslate(F, u) → F'Translate(L_2, v') → L_{19}Translate(L_1, v') → L_{20}Translate(L_3, v') → L_{21}Translate(L_4, v') → L_{22}Translate(L_5, v') → L_{23}Translate(L_6, v') → L_{24}Translate(L_7, v') → L_{25}Translate(L_8, v') → L_{26}Translate(L_9, v') → L_{27}Translate(L_{10}, v') → L_{28}Translate(L_{11}, v') → L_{29}Translate(L_{12}, v') → L_{30}Translate(L_{13}, v') → L_{31}Translate(L_{14}, v') → L_{32}Translate(L_{15}, v') → L_{33}Translate(L_{16}, v') → L_{34}Translate(L_{17}, v') → L_{35}Translate(L_{18}, v') → L_{36}Translate(D, v') → D'_3Translate(A, v') → A'_4Segment(D'_3, A'_4) → g'_3Translate(D', v') → D''_2Translate(A', v') → A''_3Segment(D''_2, A''_3) → g''_2Translate(D'_1, v') → RTranslate(A'_1, v') → SSegment(R, S) → kTranslate(D'', v') → D'''_2Translate(A'', v') → A'''_2Segment(D'''_2, A'''_2) → g'''_2Translate(C, v') → C'_1Translate(E, v') → E'_1Segment(C'_1, E'_1) → h'_1Translate(D''', v') → TTranslate(A''', v') → USegment(T, U) → lTranslate(D'_2, v') → VTranslate(A'_3, v') → WSegment(V, W) → mTranslate(D''_1, v') → ZTranslate(A''_2, v') → A_1Segment(Z, A_1) → nTranslate(J, v') → J'Translate(K, v') → K'Segment(J', K') → i'Translate(D'''_1, v') → B_1Translate(A'''_1, v') → C_1Segment(B_1, C_1) → pTranslate(C', v') → C''Translate(E', v') → E''Segment(C'', E'') → h''Translate(L, v') → L'Translate(M, v') → M'Segment(L', M') → j'Translate(B, v') → B'_4Translate(B', v') → B''_1Translate(B'_1, v') → D_1Translate(A'_2, v') → E_1Translate(B'_2, v') → F_1Translate(A''_1, v') → G_1Translate(F, v') → F'_1Translate(B'_3, v') → H_1Translate(B'', v') → B'''Translate(N, v') → N'Translate(O, v') → O'Translate(P, v') → P'Translate(Q, v') → Q'Translate(F', v') → F''