Exploring Hyperbola with Arithmetic Mean and Similarity Transformation

This GeoGebra example demonstrates a dynamic construction involving a hyperbola, arithmetic mean, and similarity transformations (rotation and scaling). It visualizes how geometric measures such as area, circumference, and angles relate to the arithmetic mean under transformations. Core mathematical concepts include arithmetic mean, similarity transformation, hyperbola, cosine, and angle/arc measures. The construction uses commands like Point, Ray, Circle, Segment, Rotate, Angle, CircleArc, CircleSector, Textfield, Area, Circumference, and FractionText. Interactive input boxes allow users to adjust parameters and observe changes in the hyperbola and associated metrics. Suitable for high school or early college students studying conic sections, transformations, and mean-related geometry, this example supports inquiry-based learning and dynamic exploration.