Tom Rocks Maths | Twos-Day Tuesday: 22 Slices of Pizza with Six Cuts @TomRocksMaths | Uploaded 2 years ago | Updated 6 minutes ago
Further explanation of the "pizza-cutting problem" presented by Tom in the 'Twos-Day Tuesday' video @standupmaths: youtu.be/Ffa8-S_71xo?t=1778
Dr Tom Crawford is a mathematician at the University of Oxford based at St Edmund Hall.
Given a circle, what is the maximum number of pieces that can be produced with n cuts? The key to the solution is maximising the number of new regions that are created with each successive cut, which means crossing as many of the previous cuts as possible.
By looking at the pattern for some examples at small values of n, we derive a recursive formula for the general case which is then simplified using Gauss' formula for the sum of the first n natural numbers.
At the end Tom attempts to cut an actual pizza into 22 pieces with only 6 cuts... SEND IN PHOTOS OF YOUR ATTEMPTS.
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
Thanks to:
Matt Parker
Steve Mould
Brady Haran
damonmensch
Spongebob Squarepants/Nickelodeon
All images used under a fair usage policy.
Spongebob Squarepants images copyright Nickelodeon.
Cricket sounds - damonmensch: freesound.org/people/damonmensch/sounds/121511
Further explanation of the "pizza-cutting problem" presented by Tom in the 'Twos-Day Tuesday' video @standupmaths: youtu.be/Ffa8-S_71xo?t=1778
Dr Tom Crawford is a mathematician at the University of Oxford based at St Edmund Hall.
Given a circle, what is the maximum number of pieces that can be produced with n cuts? The key to the solution is maximising the number of new regions that are created with each successive cut, which means crossing as many of the previous cuts as possible.
By looking at the pattern for some examples at small values of n, we derive a recursive formula for the general case which is then simplified using Gauss' formula for the sum of the first n natural numbers.
At the end Tom attempts to cut an actual pizza into 22 pieces with only 6 cuts... SEND IN PHOTOS OF YOUR ATTEMPTS.
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
Thanks to:
Matt Parker
Steve Mould
Brady Haran
damonmensch
Spongebob Squarepants/Nickelodeon
All images used under a fair usage policy.
Spongebob Squarepants images copyright Nickelodeon.
Cricket sounds - damonmensch: freesound.org/people/damonmensch/sounds/121511
