Mechanics and Curves in Mathematical History

Explore the fascinating intersection of mechanics and curves in this comprehensive 58-minute lecture from the Math History series. Delve into the evolution of motion laws, from Oresme and Galileo to Newton's groundbreaking work. Examine the relationships between distance, velocity, and acceleration in trajectories, and discover how the calculus opened new avenues for 17th and 18th-century mathematicians. Investigate non-algebraic curves like the catenary, cycloid, and lemniscate, understanding their significance in physics and mathematics. Learn about the vibrating string problem, Euler's elastica, and the modern Bézier curves. Gain insights into the historical development of curve theory and its practical applications in mechanics, from ancient times to the 20th century.

Mechanics & Curves
Distance, velocity
Acceleration
Forces
Catenary curve - Shape of a hanging chain
Parabola
Cycloids and Epicycles Ptolemy
Parametrization of the cycloid
Brachistochrone shortest time curve
Lemniscate of Bernoulli Jacob
Vibrating string
Wave equation
Euler - Elastica
Bezier curves 1960
Quadratic curves parabola