Today in History – January 26, 1697- Isaac Newton solves Bernoulli’s brachistochrone problem, inventing the “calculus of variations”. The story goes that Jean Bernoulli gave Isaac Newton a challenge solve the following problem in six months:
We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination in the briefest time.
Rather than take 6 months, Newton is reported to have solved the problem the next day. However, the solution, which is a segment of a cycloid, was solved, in part, by Leibniz, L’Hospital, Newton and the two Bernoullis. In fact, there appears to have been quite a lively, and in some cases bitter, debate about the fine points of the solution. Regardless, the challenge was to provide the seed for further development of the theory of calculus of variation used in a wide range of engineering problems, such as optimal control and optimization.
Also on this date in 1905, Cullinan Diamond (“Star of Africa”), the largest diamond ever found at the time, is unearthed. On January 26, 1926, Scottish Engineer John Baird gives first public demonstration of television in London. And in 1992, Americans with Disabilities Act went into effect. Check out the Engineering Pathway’s resources on teaching and learning for persons with disabilities.