Mechanics and Curves 
Mechanics and Curves
by UNSW / N.J. Wildberger
Video Lecture 20 of 32
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Date Added: January 19, 2015

Lecture Description

The laws of motion as set out by Newton built upon work of Oresme, Galileo and others on dynamics, and the relations between distance, velocity and acceleration in trajectories. With Newton's laws and the calculus, a whole new arena of practical and theoretical investigations opened up to 17th and 18th century mathematicians, such as the Bernoulli family (Johann, Jacob, Daniel, Nicholas, etc), Euler, Huygens and others. Non-algebraic curves played a prominent role, such as the catenary, the shape of a hanging chain, the cycloid, which become famous as both the curve of quickest descent and the curve of equal time descent, and the lemniscate which would play a major role in the theory or elliptic integrals, and gives us our sign for infinity.We also discuss some other curves that played a role in mechanics, in particular the vibrating string studied by d'Alembert, and the elastica of Euler. Moving ahead a few centuries, we show that important progress in the theory of curves still happens in modern times, with the discovery of de Casteljau and Bezier, around 1960, of a new way of thinking about curves in terms of control points.

Course Index

Course Description

In this course, Prof. N.J. Wildberger from UNSW provides a great overview of the history of the development of mathematics. The course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed)Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology and hyperbolic geometry.  This course is meant for a broad audience, not necessarily mathematics majors. All backgrounds are welcome to take the course and enjoy learning about the origins of mathematical ideas. Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. At UNSW, this is MATH3560 and GENS2005. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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