Mr. Roboto 4: Exploring Functions with Incircle Geometry

This example uses interactive controls and randomized constructions to visually link function relationships to measurable geometric features (including configurations related to an incircle/inscribed circle). It demonstrates how you can “find and verify my function” by observing how geometric quantities change under parameter variation. Key math concepts include exponential functions, linear functions, and quadratic functions, together with circle geometry and incircle (inscribed circle) relationships for right-triangle style configurations. It also connects the visualization to calculus via integral ideas (e.g., cumulative quantities/areas) and supports interpreting changes using percentage-style comparisons. Construction-wise, it relies on GeoGebra commands such as Textfield and Input for parameter entry, Random to generate varied points/parameters, Circle to create circular objects, and Point to place key geometric vertices. Text elements (e.g., text1, text3) and buttons (button1, button2) orchestrate the “Find My Function” workflow, while objects like g, i, A, B, C, D, E, F, H, I, J, k, p support the dynamic geometry and the computed visual readouts. Suitable for upper-secondary through introductory university learners, for function modeling, circle-and-triangle geometry, and intuitive calculus connections.