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…
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.
Mathematical Impressions: Spontaneous Stratification Why does a mixture of sand and colored sugar spontaneously separate when poured?
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: Shell Games A video explaining how some seemingly complex patterns on sea shells can be created by simple, one-dimensional, two-state cellular automata.
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: Curved and Straight? The elliptic hyperboloid is a beautiful quadratic surface that is “doubly ruled,” meaning that the surface, although curved, contains two straight lines through each point.
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: Geometry of Spaghetti Code A sculpture project built entirely with right angles combines math and art in subtle and surprising ways.
Math Boot Camp Prepares U.S. Team for International Mathematical Olympiad The Mathematical Olympiad Summer Program teaches students problem-solving techniques that will serve them throughout their mathematical careers