An Objection to Transcendental Definition: Quadrilateral Circumcircle and Rotati

This GeoGebra example demonstrates a dynamic geometric construction involving a general quadrilateral and its circumcircle, with rotations, angle measurements, and segment connections, raising an intuitive objection to the concept of a 'transcendental definition'. Core mathematical concepts include circles and circumscribed circles, general quadrilaterals, equilateral triangles, geometric transformations (rotation), symmetry, and geometric mean. The construction uses GeoGebra commands such as Circle, Point, Rotate, Angle, Segment, and Polygon, creating multiple points (A, B, C, D, G, K, H, etc.), circle c, rotated points G', G'', K', K'', angles α, β, γ, δ, and various segments and text labels. This is suitable for high school or university geometry instruction, exploring properties of geometric objects under transformations, relationships between circumcircles and polygons, and how dynamic demonstrations can test the validity of mathematical definitions.