Self Rotation Animation: Circle and Polygon Transformation

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2020-10-05 03:05

This GeoGebra example demonstrates a geometric figure rotating around a fixed point. The core mathematical concepts include rotation transformation, locus generation, properties of unit circles and polygons. Construction highlights: using Circle command to draw the base circle, Polygon to construct polygons, Line and Point to determine the rotation center, LineBisector and OrthogonalLine for auxiliary line construction, Segment for drawing connecting line segments, and Intersect to determine intersection points for trajectory tracking. Suitable for high school mathematics 'geometric transformation' chapter teaching, demonstrating that rotation preserves shape and size, and the relationship between rotation angle and arc length. Also serves as an intuitive tool for understanding locus of points on a circle.

GeoGebra Commands & Parameters

Circle(A_{1}, B_{1}) → c
Circle(B_{1}, A_{1}) → d
Intersect(c, d, 1) → B
Line(A_{1}, B_{1}) → f
Point(f) → D_{1}
Circle(D_{1}, Radius[d]) → e
Intersect(e, f, 1) → E
Circle(E, Radius[e]) → g
Intersect(e, g, 2) → C
Intersect(d, f, 1) → A
Intersect(c, f, 1) → H
Intersect(g, f, 2) → D
Polygon(A_{1}, B, C, D_{1}) → q1, a, c_1, f_1, d_1
Polygon(A_{1}, B, C, D_{1}) → q2, a_1, c_2, f_2, d_2
LineBisector(c_2) → h
OrthogonalLine(B, d_2) → i
Intersect(i, d_2) → F
Segment(B, F) → j
LineBisector(j) → k
Intersect(h, k) → P
Circle(P, D_{1}) → p

AI Drawing Prompt Reference

Draw an animation of a circle and a square rotating around a fixed point. The circle's center is fixed at the square's center. As the square rotates, both the circle and the square rotate. During rotation, the vertices of the square move along the circumference of the circle. The animation demonstrates how rotation preserves shape and size, and the relationship between rotation angle and arc length.

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