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: Curved and Straight? By George Hart 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: Spontaneous Stratification By George Hart Why does a mixture of sand and colored sugar spontaneously separate when poured?
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: 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: 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: Goldberg Polyhedra By George Hart 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: 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