Division of a Pizza Slice I: Dynamic Ratio and Derivative Visualization

① This example demonstrates how to divide a pizza slice (a circular sector) into proportional parts, and dynamically visualizes how the division ratio, angles, and areas change. ② Core mathematical concepts include sector area, angle proportion, percentages, right-triangle trigonometry, and the idea of derivative as a rate of change when a slider adjusts parameters. ③ Construction highlights: using GeoGebra commands such as Rotate, CircleSector, Circle, Segment, and Intersect; objects include center, radius, angle variable θ, division points A/B/C, and text objects (text1–text9) for live numeric feedback; a slider controls the angle or ratio, and a button may reset or toggle states. ④ Suitable for upper secondary or pre-university students to explore geometric division, proportional reasoning, and the concept of derivative in a dynamic setting, ideal for math lab activities or inquiry-based learning.