Sharing cake between three
Audible (30-day trial, free audio book): https://www.audible.com/numberphile
This video features Dr Hannah Fry.
More videos with Hannah: http://bit.ly/hannah_vids
Hannah's website: http://www.hannahfry.co.uk
Her book mentioned is "The Mathematics of Love".
Envy free cake cutting (the paper mentioned): https://arxiv.org/abs/1604.03655
A clarifying note from Hannah: n^n^n^n^n^n is the maximum number of cuts in the n person case.
Something we could have made clearer... Bob's trimmed piece still carries the status of his "first choice", so if Charlie leaves it, Bob will (must) pick it... otherwise he'll pick the one that was his original "second choice"... The upshot of this is that there's no chance Alice will be left with the trimmed piece after everyone takes their first piece. And Bob remains envy free under these conditions too.
A trilogy of mathematical cake cutting videos... http://bit.ly/CakeCuttingTrilogy
Editing and animation in this video by Pete McPartlan
Discuss this video on Brady's subreddit: https://redd.it/72jyww