Muaré Effect

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2023-03-13 21:00

In collections geometriadinamica.es

The Muaré effect is a unique geometric phenomenon that describes the shape formed by the intersection points of two circles. This example demonstrates the basic characteristics of the Muaré effect, involving core mathematical concepts in geometry and geometric shapes. The construction points include using GeoGebra's Sequence command and objects such as radio, A, list1, B, list2, list3, and a. Suitable for middle school and high school mathematics education, particularly for teaching geometry and graphing.

GeoGebra Commands & Parameters

Sequence(Line[(x(A) + cos(s), y(A) + sin(s)), (x(A) - cos(s), y(A) - sin(s))], s, 0°, 175.99999999999997°, 4°) → list1
Sequence(Line[(x(B) + cos(s), y(B) + sin(s)), (x(B) - cos(s), y(B) - sin(s))], s, 0°, 175.99999999999997°, 4°) → list2
Sequence(Sequence[Intersect[Element[list1, s], Element[list2, t]], s, 1, 45], t, 1, 45) → list3, {{?, (9.452293152953265, 0.6199999999999953), (6.290762677849073, 0.6199999999999953), (5.230037248170541, 0.6199999999999952), (4.694462355290021, 0.6199999999999953), (4.368890064560055, 0.6199999999999953), (4.148256180517875, 0.6199999999999953), (3.9875196447524064, 0.6199999999999953), (3.8641471927780833, 0.6199999999999953), (3.7656080450073373, 0.6199999999999953), (3.6843715807414736, 0.6199999999999953), (3.6156333380678722, 0.6199999999999953), (3.5561777794910707, 0.6199999999999953), (3.5037656756629763, 0.6199999999999952), (3.4567837474106886, 0.6199999999999952), (3.4140341184434564, 0.6199999999999953), (3.374602338969, 0.6199999999999953), (3.33777153936749, 0.6199999999999953), (3.3029646663424996, 0.6199999999999953), (3.269704321251021, 0.6199999999999952), (3.2375838715117458, 0.6199999999999953), (3.2062458635169184, 0.6199999999999953), (3.1753651385763897, 0.6199999999999952), (3.144634861423652, 0.6199999999999952), (3.113754136483123, 0.6199999999999952), (3.0824161284882963, 0.6199999999999953), (3.0502956787490216, 0.6199999999999952), (3.017035333657542, 0.6199999999999953), (2.982228460632551, 0.6199999999999952), (2.9453976610310417, 0.6199999999999952), (2.905965881556585, 0.6199999999999953), (2.863216252589352, 0.6199999999999952), (2.816234324337064, 0.6199999999999952), (2.7638222205089704, 0.6199999999999953), (2.704366661932169, 0.6199999999999953), (2.635628419258567, 0.6199999999999953), (2.5543919549927026, 0.6199999999999953), (2.4558528072219565, 0.6199999999999953), (2.332480355247632, 0.6199999999999953), (2.171743819482161, 0.6199999999999952), (1.9511099354399797, 0.6199999999999953), (1.625537644710009, 0.6199999999999953), (1.0899627518294792, 0.6199999999999953), (0.02923732215091622, 0.6199999999999953), (-3.132293152953445, 0.6199999999999953)}, {(-3.1322931529532236, 0.17999999999999544), ?, 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AI Drawing Prompt Reference

On a 2D plane, use two given center points to drive two families of circles. Around the first center, sample points on circles of fixed radius 1 by varying an angle continuously from 0° to about 176°. Around the second center, do the same to get another angle-sampled circle family. For each pair of samples, take the intersection points of the corresponding two circles and collect these intersection points. Connect the evolving intersection points in traversal order to form multiple intertwined curves, producing a Moiré effect pattern created by the intersection loci of the two circles.

The prompt above was compiled from the original drawing commands and is for reference only.