Mathematics is the ultimate game, where the players get to make up their own rules, with the only limitation being that the rules must be applied consistently. 

Mathematics is the ultimate tool for understanding the world around us. Any thing that we can accurately describe with numbers we can understand through the relationships between those numbers. 

Pascal's Triangle 
Is it possible to make Pascal's Triangle, fill a plane? See if you can beat the attempt. 
Searching for Primes 
Euclid's ancient proof that the list of primes must be infinite may be generalized into a method for searching for new primes. Can you develop this idea further? 
The Golden Mean 
The golden mean can be found using attractor methods. This show some interesting properties for number theory. 
Trisecting the Angle 
Mathematicians say it can't be done. It looks like it can! What is the error? 
Approximating Pi 
Why does this approximation technique show the value of pi to be four? 
Goldbach's Conjecture  (coming soon!) Goldbach's Conjecture has never been proven. Here are some things I learned while searching for a solution. One of these ideas might help you find a solution. 
Radiation

Radiation has nonlinear qualities. This may be observed in the current output of various types of detectors. (I observed it in the current of a neutron detector.) As a result our estimates of the impact of low level radiation may have significant errors. 
The Physical Constants 
A simple exercise with the fundamental constants of physics has some unusual implications about the universe itself. A quick approximation with a few basic concepts from physics may tell us why. 
The Lorentz Transformation (Relativity) 
The Lorentz transformation can be easily shown to fit into a wave equation. Is this mathematically trivial or physically significant? You decide. Does this demonstrate waveparticle duality? 
Gedanken

Einstein used gedanken (thought) experiments based in relativity to challenge quantum theory. Can quantum gedanken experiments challenge the limits of relativistic theory? Do you think these challenges are valid? 
Are Cars Waves? (Quantum) 
Wave equations can be utilized to analyze traffic flow. 
The Economy

Did the rich really get richer and the poor really get poorer? Use IRS reported incomes to see. Engineers: The distribution of incomes resembles a low pass filter. Look to see if you can figure out what causes the corner income. Also try to determine why the rolloff drops at higher incomes. 
Indirect Addressing 
I created realtime software to read, filter and scale analog signals, and control an I/O panel menu using an indirectly addressed data structure approach. Many beginning programmers find indirect addressing difficult. Here's an overview. 

 






