Suggestions for complicated math concepts that a child can understand My son really loves math (so do both his parents, for that matter), and does well at it in school.  I will give him math puzzles or tricks now & again, as well as introducing him to Khan Academy and some similar sites.
But I was trying to think of some advanced mathematical concepts that are typically introduced much later, simply because fewer people study them, but not because they inherently require a huge amount of previous knowledge.  I wanted to ask this community for some ideas.  Let me give some ideas of the sort of thing I was thinking of at potential ideas:


*

*graph theory

*set theory

*combinatorics

*sequences & series

*etc.


I don't mind if the concepts are tough, per se, I just don't want topics that require a huge amount of prior knowledge.  E.g., I'm a statistician, and matrices, Bayesian inference, etc. all require quite a bit of prior understanding.  Whereas, on the flip side, my son loved learning things like fibonocci sequence because it didn't require a huge set of previous knowledge.
If it matters, he is now in 4th grade, but maybe has the math knowledge of a 5th or 6th grader.
I plan on taking one concept that seems to make the most sense (and that he sounds excited about), and drill down into that one.  I don't want to hit him broadside with 4 or 5 different topics that we just cover in a cursory manner.
Thanks!
 A: From teaching and from this site, what is clear is that today's student has limited ability to visualize in three dimensions, little ability to even draw the graph of a function on xy axes on graph paper. all that has been relegated to computer screens.. My actual advice, which is what i did for my friend who had middle school and grade school children, was to get construction toys. I like Zometool, http://zometool.com/ , I like those sticks-with-magnets sets. And i really like compass and straightedge with thin cardboard for making Platonic solids. i think a fourth grader can handle a real compass without injuring himself, i did.
Anyway, from the experience with Marty's children, i do not really know what kids will do with toys if you do not guide them much. Plus, Marty's kids are all in college and going into computer science anyway. I just know, very well, what today's kids  cannot do. Surely an architect needs to be able to visualize in 3-D, preferably with lots of experience building models? Plus, perhaps more to the point, what are purely visual aspects of probability and statistics? In dimension $n,$ if a point is uniformly distributed in the cube with all coordinates $-1 \leq x_i \leq 1,$ what is the likelihood that it is in the (inscribed) unit ball?  
Let's see, stacking spheres. I would use ping pong balls, fewer uncertainties than oranges, less weight than billiard balls. Why does it not really change anything whether we start with the bottom layer arranged in a square or an equilateral triangle?
Probably enough. Write to me if you like. My site profile has enough information to get my email addresses, phone number. 
