Sum of Squares of Radial Segments via Riemann Sums

This example demonstrates how to partition the interior of a circle (or related conic context) into radial segments, compute the length of each radial segment, and form the sum of their squares. It highlights the core idea of approximating a continuous quantity by a discrete sum (Riemann-sum viewpoint). Key concepts include: circle geometry and intersection-based construction, deriving radial segment lengths from constructed points, generating sampling partitions with sequences, and interpreting upper/lower sums (Riemann sums) as a bridge toward integration of a corresponding function. Construction relies on GeoGebra commands from the provided summary: Intersect and Circle to build the circle and obtain intersection points; PointIn to ensure points lie on/in the intended region; Sequence to create the parameterized set of sample points; Flatten to organize nested sequences for aggregation; and Sum to accumulate the radial lengths (and, as modeled, their squares). Text objects (Text1, Text2) annotate the computed quantities. Suitable for high school through early university, especially for lessons on geometric construction, sequences, and the intuition behind integrals via Riemann sums.