There’s a nice area-volume question wrapped up in there.
Data Representation Resources Statistics
Applications of Government Data
This is a nice resource from The Guardian that highlights some of the ways developers are making government data accessible to citizens.
The projects include housing price analysis, roadway usage, government spending, and aggregation of community information.
The site wheredoesmymoneygo.org is especially interesting: slide the bar to your yearly income, and see just how much of your salary is spent on education, health services, defense, and other categories.
Lots of applications to play around with, and plenty of food for thought!
Resources
Fundamental Examples
Here is another nice crowd-sourced resource from MathOverflow.net: a list of fundamental examples in mathematics.
http://mathoverflow.net/questions/4994/fundamental-examples
From the premise that a single example can often shape an entire mathematical discipline, a list of such examples is generated.
The list includes examples like the harmonic series in Real and Complex Analysis; the Brachistochrone problem in Physics; the Gaussian integers in Algebra; the Platonic solids in Geometry; and the Seven Bridges of Konigsberg in Graph Theory.
This is a great resource that provides accessible entry points to a lot of advanced mathematics!
Resources Technology
Desmos, the Free Online Graphing Calculator
Desmos is a powerful, versatile, and free online graphing calculator.
Desmos combines the typical functionality of a graphing calculator with dynamic representation capabilities. The result is an intuitive and powerful tool for demonstrating and exploring mathematics.
Desmos is one of the best things to happen to math in years! It has quickly become an essential part of my math classroom.
Check out the software itself at Desmos.com.
And you can see some of the ways I use Desmos in and out of the classroom here, including resources from my Introduction to Desmos workshops.