Folding a Circle to Draw an Ellipse via Symmetry

This example demonstrates how to draw an ellipse by “folding” a circle using geometric symmetry. It connects the ellipse’s characteristic construction with mirror operations, intersections, and arc-based point generation. The key math ideas are: circle/ellipse geometric relationships, transformations via reflection (Mirror), angle- and constraint-driven constructions, and continuity through systematic point sequencing. In GeoGebra, the workflow uses core commands such as Point (defining pivotal points), Mirror (creating folded/reflected counterparts), Circle (setting the base circle), Sequence (building an ordered set of steps/points), LineBisector (constructing symmetry-related lines), Intersect (finding intersection points of constructed objects), CircleArc and CircumcircleArc (generating arc geometry), Segment and Vector (for supporting constructions), Angle (imposing angle conditions), and Take (using computed selections). The construction objects include the center O, seed points on the circle (A and its reflected A'), intermediate points generated from arc/line intersections, and the resulting locus/curve traced from the ordered construction. Suitable for secondary school exploration, geometry construction lessons, and GeoGebra-based demonstrations of transformations and curve generation.