Earlier this year the New York Times published a great series of articles on mathematics by Cornell math professor Steven Strogatz.
Strogatz does a wonderful job sharing the wonders of maths for the lay person, starting from simple counting and finishing up with more complex topics like integration, probabilities, and some of David Hilbert's work.
Here's a beautiful example from an early column: Rock Groups. The question posed is why is the sum of consecutive odd numbers always a perfect square?
1 + 3 = 41 + 3 + 5 = 91 + 3 + 5 + 7 = 161 + 3 + 5 + 7 + 9 = 25
At first glance this is an interesting observation but hard to understand... Until you look at these equations graphically:
And then it makes perfect sense!
Another favorite focuses on limits and gives an elegant application to finding the area of a circle.
A series well worth reading and, if you have any, sharing with your children.