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: The Mathematics of Juggling By George Hart 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: Symmetric Structures By George Hart 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: Making Music With a Möbius Strip By George Hart Musical chords naturally inhabit certain topological spaces, which show the possible paths that a composer can use to move between chords.
Mathematical Impressions: Knot Possible? By George Hart 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 By George Hart 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 By George Hart A video explaining how some seemingly complex patterns on sea shells can be created by simple, one-dimensional, two-state cellular automata.
Mathematical Impressions: Long Sword Dancing By George Hart 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: Geometry of Spaghetti Code By George Hart A sculpture project built entirely with right angles combines math and art in subtle and surprising ways.
Mathematical Modeling of Living Systems