Construction and Properties of the Reuleaux Triangle

This applet demonstrates the construction and geometric properties of the Reuleaux triangle, a fascinating curve of constant width formed by three circular arcs centered at the vertices of an equilateral triangle. Using GeoGebra's dynamic geometry tools, the applet walks students through the step-by-step construction process, showing how circles, points, and rotation can be combined to create this unique figure. The interactive construction makes it easy to follow each stage, from drawing the initial equilateral triangle to generating the intersecting arcs that define the Reuleaux triangle. Beyond construction, the applet explores one of the most remarkable properties of the Reuleaux triangle: its constant width. By calculating and displaying extreme coordinates in different directions, the applet provides a visual and numerical verification that the distance between any pair of parallel supporting lines remains the same regardless of orientation. This直观验证 (intuitive verification) of the equidistance property makes an abstract theorem tangible and accessible. The applet is particularly valuable for students studying geometric constructions, curve properties, and extremum problems. It bridges the gap between classical compass-and-straightedge techniques and modern dynamic geometry, helping learners see how theoretical concepts like constant width manifest in a concrete, manipulable model. Educators can use this tool in lessons on synthetic geometry, advanced Euclidean constructions, or even introductory topics in non-circular shapes and their applications. The dynamic nature of the applet invites exploration and experimentation, encouraging students to ask questions and discover properties on their own rather than passively receiving information.