Max Bill's Geometric Construction
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Paintings modeled in Geogebra
This example demonstrates Max Bill's work through geometric construction using GeoGebra commands such as Point, Polygon, Midpoint, and Segment. It involves core mathematical concepts such as coordinate geometry and geometric construction. Suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Point(yAxis) → APoint(xAxis) → BPolygon(A, B, 4) → poly1, f, g, h, i, C, DMidpoint(f) → EMidpoint(i) → FMidpoint(g) → GMidpoint(h) → HPolygon(G, H, 4) → poly2, j, k, l, m, I, JMidpoint(B, E) → KMidpoint(B, G) → LMidpoint(A, E) → MMidpoint(A, F) → NMidpoint(F, D) → OMidpoint(D, H) → PMidpoint(H, C) → QMidpoint(C, G) → RSegment(K, L) → nSegment(M, N) → pSegment(O, P) → qSegment(Q, R) → rPolygon(B, L, K) → t1, k_1, b, l_1Polygon(A, M, N) → t2, n_1, a, m_1Polygon(O, P, D) → t3, d, o, p_1Polygon(R, Q, C) → t4, c, r_1, q_1Polygon(K, L, G, E) → q1, k_2, l_2, g_1, ePolygon(M, E, F, N) → q2, m_2, e_1, f_1, n_2Polygon(G, H, Q, R) → q3, g_2, h_1, q_2, r_2Polygon(F, O, P, H) → q4, f_2, o_1, p_2, h_2Polygon(E, F, H, G) → q5, e_2, f_3, h_3, g_3Polygon(E, F, H, G) → q6, e_3, f_4, h_4, g_4
AI Drawing Prompt Reference
Draw a complex geometric pattern composed of multiple quadrilaterals. Start by taking points A and B on the x-axis and y-axis respectively, then construct a quadrilateral with A and B as opposite vertices. Next, take the midpoints E, F, G, and H of the diagonals of the quadrilateral, and construct another quadrilateral. Using these midpoints and the vertices of the original quadrilateral, further construct multiple quadrilaterals to form the final pattern.
The prompt above was compiled from the original drawing commands and is for reference only.