A nice mathematical puzzle, with a solution anyone can understand, is to determine the direction a bicycle went when you come upon its tracks. The answer involves thinking about tangent lines, geometric constraints and the bicycle’s steering mechanism.

# Search Results for: "mathematical impressions"

### Mathematical Impressions: Symmetric Structures

It is an unexplained fact that objects with icosahedral symmetry occur in nature only at microscopic scales. Examples include quasicrystals, many viruses, the carbon-60 molecule, and some beautiful protozoa in the radiolarian family.

### Mathematical Impressions: Attesting to Atoms

Can you combine simple observations and mathematical thinking to show that atoms exist?

### Mathematical Impressions: Knot Possible?

The mathematics of knot theory says that a simple loop and a trefoil are fundamentally different knots. But is that all there is to the question?

### Mathematical Impressions: The Surprising Menger Sponge Slice

The Menger Sponge, a well-studied fractal, was first described in the 1920s. The fractal is cube-like, yet its cross section is quite surprising. What happens when it is sliced on a diagonal plane?