Mathematical Impressions
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.
November 14, 2014
Mathematical Impressions: Curved and Straight?
By George Hart
![Hands holding the top and bottom of a hyperboloid model](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11210539/Hyperboloids-Still.jpg?auto=format&q=90&fit=crop&w=590&h=330)
March 27, 2015
Mathematical Impressions: The Golden Ratio
By George Hart
![Two hands hold a swirly shell that abides by the Golden Ratio](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/12024158/Golden-Ratio-Thumb.jpg?auto=format&q=90&fit=crop&w=590&h=330)
September 16, 2014
Mathematical Impressions: Long Sword Dancing
By George Hart
![Four popsicle sticks intertwined](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11210358/longsword_thumb3.jpg?auto=format&q=90&fit=crop&w=590&h=330)
May 23, 2014
Mathematical Impressions: Spontaneous Stratification
By George Hart
![Measuring cup with pink sand inside it and a wooden spoon in the sand](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11210151/spontaneous_stratification_thumb.jpg?auto=format&q=90&fit=crop&w=590&h=330)
March 20, 2014
Mathematical Impressions: The Bicycle Pulling Puzzle
By George Hart
![Illustration of wheel and pedal/pulley mechanism](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11210030/bike_pull_thumb3.jpg?auto=format&q=90&fit=crop&w=590&h=330)
February 03, 2014
Mathematical Impressions: Change Ringing
By George Hart
![Digital visualization of all the permutation combinations of 1234, connected with lines](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11205930/screenshot_384.jpg?auto=format&q=90&fit=crop&w=590&h=330)
October 07, 2013
Mathematical Impressions: Art Imitates Math
By George Hart
![Corner of 5 different motherboards fused together with red coils at the edges](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11200123/bridges_thumb.jpg?auto=format&q=90&fit=crop&w=590&h=330)
August 12, 2013
Mathematical Impressions: Making Music With a Möbius Strip
By George Hart
![Digital image of Mobius music](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11205122/Mobius-Music-thumb.jpg?auto=format&q=90&fit=crop&w=590&h=330)
June 18, 2013
Mathematical Impressions: Goldberg Polyhedra
By George Hart
![Digital image of green and yellow Goldberg Polyhedra](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11205106/mseo_goldberg_polyhedra_thumb2.jpg?auto=format&q=90&fit=crop&w=590&h=330)
May 09, 2013
Mathematical Impressions: The Mathematics of Juggling
By George Hart
![Mathematics of juggling 3 balls at different heights](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/12025946/Screen-Shot-2017-05-22-at-3.01.29-PM.png?auto=format&q=90&fit=crop&w=590&h=330)
April 16, 2013
Mathematical Impressions: Bicycle Tracks
By George Hart
![Digital bicycle drawing labelled with the wheelbase, head angle and rake](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11205047/bicycletracks_thumb.jpg?auto=format&q=90&fit=crop&w=590&h=330)
March 15, 2013
Mathematical Impressions: Symmetric Structures
By George Hart
![Hand holding a complex symmetric shape](https://simonsfoundation.imgix.net/wp-content/uploads/2017/07/11204533/SymmetricStructuresSpan3.jpg?auto=format&q=90&fit=crop&w=590&h=330)
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