The brachistochrone problem posed by Bernoulli and its solutionhighlights one of the most famous experiments in physicswhich illustrates the variational principle. This pedagogicalstudy is designed to ignite a classroom discussion on the variationalproblem. We overview the Euler–Lagrange formalismof the variational principle and obtain the solution to thebrachistochrone problem. We demonstrate the success of thevariationalmethod using brachistochronemodels which werefabricated specially for this purpose.

In this article, we discuss the Belousov–Zhabotinsky (BZ) reactionand its relation with the Oregonator model of chemicalreactions. The Oregonator model has a limit cycle, andthe BZ reaction shows chemical oscillations. We comparethe time series obtained from the Oregonator model, with thetime series obtained from an experimental study of the BZ reactionand show that the qualitative behaviour is similar. Wealso construct the limit cycle from the experimental data usingthe Takens’ embedding theorem and compare it with thelimit cycle from the Oregonator model. We conclude with ademonstration of the spatio-temporal patterns which can beseen in the two-dimensional version of this system.