Well, WolframAlpha (aka "online mathematica") surely qualifies as lightweight, has a bit of a learning curve and is by design easy to use, though it can misinterpret your input if you don't use the commands directly. It can certainly do everything a desktop calculator can. That said, it is unfortunately no longer free, and most of the cool advanced features (data analysis, etc..) are not available to guests...
You could use LaTeX/Tikz to draw polygons and possibly graphs, with no limitations, though the learning curve is quite punishing. You can then save and even share the text scripts everywhere. Not sure it qualifies as an "elementary tool" and it's not exactly lightweight, though I'm sure web services exist. But the "calculator" aspect is obviously lost, unless you are insane and want to use the preprocessor to compute stuff.
Edited by Bacterius, 04 February 2013 - 06:05 AM.
The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.
- Pessimal Algorithms and Simplexity Analysis