Math Encounters -- A Surreptitious Sequence: The Catalan Numbers

What's so special about the sequence 1, 1, 2, 5, 14, ...? First described by Euler in the 1700s and later made famous by Belgian mathematician Eugène Catalan, the Catalan numbers take on a variety of different guises as they provide the solution to numerous combinatorial problems. Join mathematician Alissa Crans, recent Director of Educational and Outreach Activities at MSRI and current Loyola Marymount Associate Professor, as she explores some of the many ways in which the Catalan numbers are hidden throughout mathematics. Alissa will be introduced by John Ewing, president of Math for America.

Math Encounters is a public presentation series celebrating the spectacular world of mathematics and presented by the Simons Foundation and the National Museum of Mathematics.

[teaganm]

this has literally saved me and my grades for my maths assignment, thank you thank you thank you!

[CandidDate]

an electric spark uses somehow these numbers, albeit maybe in 3 dimensions:
The spark travels from one point to another, but randomly goes up or down and side to side along the way. Like the mountain peak example.

[shashanksingh]

Generating function for Catalan Number is ( 1 - sqrt( 1 - 4x))/ (2x) . 2 in denominator is missing in the video.

[SivaramakrishnanSivakumar]

At 53:23 the generating function for Catalan numbers, misses a 2 in the denominator . See wikipedia

[shashanksingh]

Generating function for Catalan Number is 2 in denominator is missing in the video.

[davidjames]

Why were ancient Mathematicians mostly men? Answer: cuz u don't need to know much math to work in the kitchen (2 cups of flour, 1 cup of sugar...) or in the bedroom (position 69, position 140...).