How many triangles do you see?

Sure, you can count them. I did, and, er, I missed a few. Or you can take one of the approaches suggested by the mathematics professors that Andrew Daniels interviewed in Popular Mechanics:

"I would approach this just like one approaches any mathematical problem: reduce it and find structure," says Sylvester Eriksson-Bique, Ph.D., a postdoctoral fellow with the University of California Los Angeles's math department.