Roulette curves represent a fascinating class of curves in mathematics, generated by tracing a fixed point on one curve as it rolls without slipping along another curve. The most famous example is the cycloid, created when a circle rolls along a straight line. 
These curves have significant applications in physics and engineering, particularly in gear design and optical systems. The study of roulette curves dates back to the 17th century, with contributions from mathematicians like Galileo and Bernoulli.
Modern applications include robotics path planning and animation algorithms. The mathematical properties of roulette curves continue to inspire researchers in computational geometry and differential equations. |
