The graphic result of a quadratic function

Quadratic functions also allow for a fun afternoon combining the jQuery form plugin with the jpgraph PHP library. I started out with a simple PHP function to produce a range of f(x) values for any set of values x. I then built a form to allow any value for a, b and c to be input as well as the maximum and minimum for x and the steps that x takes. Once that was working, I passed the results into two arrays and passed those to jpgraph which produces a graphical image on the fly and stores it on the server. Finally, to avoid page refreshes, I wrapped the form around the jQuery ‘plugin’ (can these properly be called plugins? I suppose so…) The result is a simple and relatively intuitive visual demonstration of the relationship between mathematics and geometry. In fact, expanding that out, the relationship is actually between mathematical logic, computation and optics – but that gets us into a kind of crazy Turing territory and lines have to be drawn somewhere.

Try it out here

For the future, I would like to be able to produce more accurate and extensible graphs for larger number ranges, and to plug the whole thing into calculus, to really push the spatial theme. But this is something of a start and it is perhaps the simplest demonstration of the more general relationship.

While I am writing about Vivid, I ought to briefly mention the nifty jQuery vertical scroller that I have installed on the right hand side column for the front page of the site. The editor has long wanted to show off the covers of all past issues, and I thought this was the most economical and user-friendly way to do it. I also linked each cover to the subscriptions page on the site, because it’s always worth getting the best economical advantage out of any addition.