Constructing an Ellipse as an Envelope via Correspondence

This example demonstrates how an ellipse can be constructed using the envelope idea: a family of corresponding lines (or segments) is generated, and their envelope forms the target ellipse. The key math concepts include ellipse geometry, the notion of an envelope (包络曲线), and correspondence-driven construction. It also connects to tools such as arithmetic mean and linear regression through how parameters and mappings are set up to relate points/lines. From the construction summary, the build is driven by Sequence to parameterize the sweep; shiftO1 and shiftO2 provide translations of construction objects; domain/range (and domainSmall/rangeSmall) specify parameter intervals; segmDown/segmUp create the line-segment elements in different directions; horLineUp/horLineDown act as horizontal helper constructs; and base points O and O1 anchor the geometry. Suitable for advanced secondary school through early university learners, especially for lessons on geometric construction, envelope curves, and correspondence/parameter-based visualization.