Mobilis in mobili symmetry (generalised)
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This example demonstrates the 'Mobilis in mobili' symmetry. It involves key concepts such as symmetry and geometric transformations. Using GeoGebra commands like Circle, Point, Segment, Rotate, etc., a dynamic geometric figure is constructed. Suitable for high school and above students or teachers for teaching or self-study.
GeoGebra Commands & Parameters
Circle(D, d) → hPoint(h) → ECircle(A, a) → ePoint(e) → BCircle(B, b) → fPoint(f) → CSegment(C, E) → sCircle(C, c) → gPoint(g) → GSegment(G, E) → pRotate(G, 90°, C) → G'Midpoint(G', G) → PLine(C, P) → j_1Intersect(g, j_1, 2) → QSegment(Q, E) → p_1Segment(G', E) → qLine(G', C) → kIntersect(g, k, 2) → IMidpoint(G, I) → NLine(C, N) → i_1Intersect(g, i_1, 2) → OSegment(O, E) → t_1Segment(I, E) → nLine(G, C) → iIntersect(g, i, 2) → HMidpoint(H, I) → LLine(C, L) → f_1Intersect(g, f_1, 2) → MSegment(M, E) → s_1Midpoint(G', H) → JLine(C, J) → tIntersect(g, t, 2) → KSegment(K, E) → r_1Segment(H, E) → rAngle(G, C, G') → αSegment(C, G') → jSegment(G, H) → lSegment(G', I) → mSegment(C, K) → k_1Segment(C, O) → l_1Segment(C, Q) → m_1Segment(C, M) → n_1Polygon(G, Q, G', K, H, M, I, O) → poly1, g_1, q_1, g', k_2, h_1, m_2, ı, o
AI Drawing Prompt Reference
Draw a dynamic geometric figure demonstrating 'Mobilis in mobili' symmetry. Start by creating a circle and points on it, then draw new circles centered at these points. Connect specific points to form segments, and use rotations and symmetry operations to build a complex geometric structure. Finally, connect multiple points and segments to form a polygon, highlighting the core concepts of symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.