Kepler Right Triangle (Kepler-Dreieck): Proportions via Construction

This example constructs a special right-triangle configuration (Kepler-Dreieck) to demonstrate how angle-controlled quantities lead to stable proportions among side-related segments, and how these relationships remain interpretable under geometric scaling/reshaping. It focuses on core ideas such as right-triangle geometry, perimeter/segment measurements, proportional relationships, and triangle trig connections driven by an angle parameter (e.g., φ) and derived lengths (denoted by variables like c, a, b and additional segment lengths). Construction-wise, it uses Polygon to form the triangular/polygonal outlines, Segment to define the measurable edges and connecting lines, and Intersect to compute key intersection points that determine the rest of the configuration. Text labels (Text1–Text4) provide annotations for the constructed lengths/angles, while parameters and derived objects (including symbols like d1, d2, f, g, h, i, j, k, l, m, n, p) encode the relationships revealed by the geometry. Suitable for high-school geometry enrichment, trig modeling, and hands-on GeoGebra-based teaching of “angle → side measures → proportion” reasoning.