Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

The problem involves an equilateral triangle rolling without slipping around a square of side length 1, tracing a specific path. As the triangle rolls, the marked point on it moves rotationally for a total of 210 degrees along part of a radius 1 circle. The movement repeats in segments around the square, ultimately returning to its initial position after completing this rotation four times (or a total of eight, 210-degree rotations). Calculating the total length traveled by the marked point involves summing these, resulting in a path length of \( \frac{28\pi}{3} \).

Keywords

equilateral triangle

rolling motion

square path

rotational movement

path length calculation