Mathematical Impressions: The Bicycle Pulling Puzzle If you pull straight back on the lower pedal of your bicycle, will the bike move forward or backward? This classic puzzle has a surprising twist.
Mathematical Impressions: Attesting to Atoms Can you combine simple observations and mathematical thinking to show that atoms exist?
Mathematical Impressions: Bicycle Tracks 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…
Mathematical Impressions: Spontaneous Stratification Why does a mixture of sand and colored sugar spontaneously separate when poured?
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…
Mathematical Impressions: The Mathematics of Juggling Juggling has advanced enormously in recent decades, since mathematicians began systematically investigating the possible patterns of non-colliding throws. As part of this research, many new possibilities have been discovered for…
Mathematical Impressions: Goldberg Polyhedra Because of their aesthetic appeal, organic feel and easily understood structure, Goldberg polyhedra have a surprising number of applications ranging from golf-ball dimple patterns to nuclear-particle detector arrays.
Mathematical Impressions: Making Music With a Möbius Strip Musical chords naturally inhabit certain topological spaces, which show the possible paths that a composer can use to move between chords.
Mathematical Impressions: Long Sword Dancing How do long sword dances produce stable patterns of interwoven segments? What are the possible variations? Explore the mathematics of this traditional art form.