The Cross Ratio - Numberphile

One of the most famous free kicks ever taken - but how far from the goal was Brazil's Roberto Carlos?
More links & stuff in full description below ↓↓↓

Discussed by Federico Ardila from San Francisco State University.
More Federico videos: http://bit.ly/Federico_Numberphile

More football/soccer videos by Numberphile: http://bit.ly/Football_Numberphile

The goal was scored by Carlos in a 1-1 drawn between France and Brazil at the Stade de Gerland, Lyon, on 3 June 1997 - it was game one of the "1997 Tournoi de France".

Goal animation by Pete McPartlan

Discuss this video on Brady's subreddit: https://redd.it/8wkcqh

Patreon: http://www.patreon.com/numberphile

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/

And support from Math For America - https://www.mathforamerica.org/

NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub

Videos by Brady Haran

Numberphile T-Shirts: https://teespring.com/stores/numberphile

Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/

Brady's latest videos across all channels: http://www.bradyharanblog.com/

Sign up for (occasional) emails: http://eepurl.com/YdjL9

Special thanks to these Patreon supporters:
Jeremy Buchanan
Arjun Chakroborty
Jeff Straathof
Susan Silver
Andy
Yana Chernobilsky
Christian Cooper
Ken Baron
Bill Shillito
Ben
Tony Fadell
Turner Lehmbecker
Bernd Sing
Dr Jubal John
Thomas Buckingham
Adam Savage
Roman Pinchuk
James Bissonette
john buchan
Joshua Davis
Steve Crutchfield
Jon Padden
Jean-Pierre Bergeron
Kristo Käärmann
Valentin-Eugen Dobrota
D Hills
Eric Mumford
Charles Southerland
Arnas
Ian George Walker
Tracy Parry
George Greene
Igor Sokolov
Alfred Wallace
Bodhisattva Debnath