![Mathematical Impressions: Long Sword Dancing [Video]](https://static.scientificamerican.com/sciam/cache/file/44F21AA1-62C9-40A3-B0928E48029EDAD7_agenda.png?w=275&h=154&fit=crop)
Mathematical Impressions: Long Sword Dancing [Video]
This art form produces stable patterns of interwoven segments that are mathematically rich
Stories by George Hart
![Mathematical Impressions: Spontaneous Stratification [Video]](https://static.scientificamerican.com/sciam/cache/file/602C7E07-FE51-4D2B-91C1524C2029C8F8_agenda.jpg?w=275&h=154&fit=crop)
Mathematical Impressions: Spontaneous Stratification [Video]
Why does a mixture of sand and colored sugar spontaneously separate when poured?
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
The Mathematics of Change Ringing and Peal Bells
Change ringing, in which a band of ringers plays long sequences of permutations on a set of peal bells, is a little-known but surprisingly rich and beautiful acoustical application of mathematics
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: Goldberg Polyhedra [Video]](https://static.scientificamerican.com/sciam/cache/file/0F8EDC49-68C4-4CD7-97501E54A5CB7924_agenda.jpg?w=275&h=154&fit=crop)
Mathematical Impressions: Goldberg Polyhedra [Video]
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
Follow That Bike!
The direction a bicycle has traveled can be determined by examining its tracks and thinking about tangent lines, geometric constraints and the bike's steering mechanism
![Mathematical Impressions: An Exploration of Symmetric Structures [Video]](https://static.scientificamerican.com/sciam/cache/file/7967C607-62ED-491A-9503C5DF0239AB4E_agenda.jpg?w=275&h=154&fit=crop)
Mathematical Impressions: An Exploration of Symmetric Structures [Video]
Objects with icosahedral symmetry occur in nature only at microscopic scales, including quasicrystals, many viruses and some beautiful protozoa in the radiolarian family
![The Real Power of Crystals: Attesting to Atoms [Video]](https://static.scientificamerican.com/sciam/cache/file/496E8F9C-67CF-4328-A64DF4E7DE3D3130_agenda.jpg?w=275&h=154&fit=crop)
The Real Power of Crystals: Attesting to Atoms [Video]
The exact angles of crystals reveals their underlying structure as given by repeating lattices of atoms and molecules, as explained in this video by geometer George Hart
![Mathematical Impressions: The Surprising Menger Sponge Slice [Video]](/public/resources/icon__SA-logo-placeholder--rect-3166a74694258e68c9c9fd6e14c45ff6.jpg){kind=icon}
Mathematical Impressions: The Surprising Menger Sponge Slice [Video]
What happens when this well-studied cube-like fractal is sliced on a diagonal plane? Try to predict the solution the puzzle before minute 3:25 in this video
![Mathematical Impressions: Can You Turn a Rubber Band into a Knot? [Video]](https://static.scientificamerican.com/sciam/cache/file/B0516128-3DE7-4A97-8110428295C9CF46_agenda.jpg?w=275&h=154&fit=crop)
Mathematical Impressions: Can You Turn a Rubber Band into a Knot? [Video]
Theory suggests it is impossible, but geometer George Hart shows that the band's thickness can help you solve this puzzle