Arc Length: Quick Investigation

This GeoGebra example dynamically explores the relationship between radian measure, arc length, and radius. It demonstrates that for a central angle measured in radians, the arc length equals the radius times the angle (s = rθ), providing a visual and interactive understanding of why radians are a natural unit for angles. The construction uses commands such as Circle, CircleArc, Intersect, Point, Segment, Distance, and Angle to build a circle with a movable point on the circumference, creating an arc whose length and corresponding angle are displayed. It is suitable for high school or introductory college students learning trigonometry, radian measure, or circle geometry, and can be used for classroom demonstrations or self-guided exploration.