Mathematical Impressions

SIMONS FOUNDATION - Advancing Research in Basic Science and Mathematics

How do you turn a rubber band into a knot? What happens when you slice a Menger Sponge on a diagonal plane? What is the math behind juggling? In this video series, George Hart illuminates mathematical concepts and surprising hidden geometries that may be found in the world around us.

 

 

 

Mathematical Impressions

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. http://www.simonsfoundation.org/multimedia/shell-games/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Art Imitates Math
The art exhibition at the annual Bridges Conference showcases a wide range of artworks inspired by mathematical thinking. http://www.simonsfoundation.org/multimedia/mathematical-impressions-art-imitates-math/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Attesting to Atoms
Can you combine simple observations and mathematical thinking to show that atoms exist? http://www.simonsfoundation.org/multimedia/attesting-to-atoms/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Geometry of Spaghetti Code 2
Spaghetti Code Assembly http://www.simonsfoundation.org/multimedia/geometry-of-spaghetti-code/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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 lines, geometric constraints and the bicycle's steering mechanism. http://www.simonsfoundation.org/multimedia/mathematical-impressions-bicycle-tracks/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Regular Polylinks
A video illustrating the beautiful geometry behind symmetrical linkages of regular polygons. http://www.simonsfoundation.org/multimedia/regular-polylinks/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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? http://www.simonsfoundation.org/multimedia/mathematical-impressions-knot-possible/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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. http://www.simonsfoundation.org/multimedia/mathematical-impressions-multimedia/the-bicycle-pulling-puzzle/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Change Ringing
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. http://www.simonsfoundation.org/multimedia/mathematical-impressions-change-ringing/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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 a diagonal plane? http://www.simonsfoundation.org/multimedia/mathematical-impressions-the-surprising-menger-sponge-slice/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Geometry of Spaghetti Code
A sculpture project built entirely with right angles combines math and art in subtle and surprising ways. http://www.simonsfoundation.org/multimedia/geometry-of-spaghetti-code/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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. http://www.simonsfoundation.org/multimedia/mathematical-impressions-making-music-with-a-mobius-strip/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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 the radiolarian family. http://www.simonsfoundation.org/multimedia/symmetric-structures/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
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. http://www.simonsfoundation.org/multimedia/mathematical-impressions-goldberg-polyhedra/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm
Mathematical Impressions: Printing 3-D Models
George Hart describes in this video how to create physical models of mathematical objects, surveying some examples of surfaces and polytopes. http://www.simonsfoundation.org/multimedia/3-d-printing-of-mathematical-models/
Author: SimonsFoundation
Posted: May 22, 2014, 2:04 pm

 

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