Pizza theorem
In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way.
Let p be an interior point of the disk, and let n be a number that is divisible by four and greater than or equal to eight. Form n sectors of the disk with equal angles by choosing an arbitrary line through p, rotating the line n/2 − 1 times by an angle of 2π/n radians, and slicing the disk on each of the resulting n/2 lines. Number the sectors consecutively in a clockwise or anti-clockwise fashion. Then the pizza theorem states that:
The sum of the areas of the odd numbered sectors equals the sum of the areas of the even numbered sectors (Upton 1968).
The pizza theorem is so called because it mimics a traditional pizza slicing technique. It shows that, if two people share a pizza sliced in this way by taking alternating slices, then they each get an equal amount of pizza.

This is an excerpt from the article Pizza theorem from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Pizza theorem at en.wikipedia.org was accessed 1,362 times in the last 30 days. (as of: 12/16/2013)
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Pizza theorem - Wikipedia, the free encyclopedia
In elementary geometry, the Pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. Let p be an interior point of the ...
en.wikipedia.org/wiki/Pizza_theorem
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Pizza Theorem -- from Wolfram MathWorld
Pizza theorem. If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate ...
mathworld.wolfram.com/PizzaTheorem.html
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Pizza Slices -- Math Fun Facts
Take a pizza and pick an arbitrary point in it. Suppose you cut the pizza into 8 slices by cutting at 45 degree angles through that point, and color the alternate ...
www.math.hmc.edu/funfacts/ffiles/10001.2.shtml
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geometry - Proof of the Pizza Theorem - Mathematics Stack Exchange
Nov 26, 2013 ... How do we prove the Pizza theorem? I tried a coordinate bash (I also involved the concept of finding areas through definite integration).
math.stackexchange.com/questions/581895/proof-of-the-pizza-theorem
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The Pizza Theorem – Futility Closet
Oct 22, 2011 ... The Pizza theorem. http://commons.wikimedia.org/wiki/File:Pizza_theorem_1. If you're sharing a pizza with another person, there's no need to ...
www.futilitycloset.com/2011/10/22/the-pizza-theorem/
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Pizza - solution
We have first to prove the Pizza theorem. If we cut a disk (a pizza...) from any interior point by any 4 lines 45 degrees apart, the total area of even numbered ...
mathafou.free.fr/pbg_en/sol116.html
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Of Cheese and Crust: A Proof of the Pizza Conjecture and Other ...
The following theorem, which provides a precise solution to this question, had its genesis in ... Our contribution to the Cheese Pizza theorem will be to settle the ...
www.cs.umd.edu/~gasarch/BLOGPAPERS/pizza.pdf
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57. THE PIZZA THEOREM Jeremy, Michael, Jeremy K., Andrew and ...
Theorem. If a circular pizza is cut into 4n slices by 2n concurrent cuts (which run right across the pizza) at equal angles to each other, and n people share the ...
web.maths.unsw.edu.au/~mikeh/webpapers/paper57.pdf
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How to equally share a pizza? | Entangled States
Dec 14, 2009 ... Here the Pizza theorem says that if you cut the pizza with 3, 7, 11, 15… cuts, and no cut goes through the centre, then the person who gets the ...
entangledstates.org/2009/12/14/how-to-equally-share-a-pizza/
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pizza theorem - Wolfram Alpha
www.wolframalpha.com/input/?i=pizza+theorem
Search results for "Pizza theorem"
Pizza theorem in science
[PDF]Of Cheese and Crust: A Proof of the Pizza Conjecture and Other ...
Our contribution to the Cheese Pizza theorem will be to ...... RICK MABRY received his Ph.D. from the University of South Florida, Tampa, during the previous ...
Pizza theorem - Wikipedia, the free encyclopedia
In elementary geometry, the Pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. Let p be an interior point of the ...
Pizza Theorem -- from Wolfram MathWorld
Pizza theorem. If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate ...
More on the pizza theorem
University of Adelaide Library ... The University of Adelaide Australia. The University of Adelaide Library ... Title: More on the Pizza theorem. Author: Pearce  ...
[PDF]Pizzas, crusts and other tasty things MUMS Talk - Department of ...
Apr 30, 2010 ... The University of Melbourne. April 30 ... A pizza is divided into 2N slices by means of N straight cuts. Every cut ... Theorem (Pizza theorem 1).
The mathematics of pizza slicing » Edward Willett
(OK, maybe pizza is not the most traditional of foods, but it's still a popular ... they used to share pizza for lunch at Louisiana State University in Shreveport. ... There's been a “Pizza theorem” that postulates this since the late 1960s (naturally ).
[PDF]Sharing a pizza with a friend but not sure you are ... - Stephen Ornes
They can't think about sharing a pizza, for example, without ... were both at Louisiana State University, ... years to form the complete Pizza theorem. The first  ...
My Favorite Geometry Proof - Framingham State University
Aug 2, 2013 ... Organizer: Sarah Mabrouk, Framingham State University ... My love affair with the so-called Pizza theorem is now entering its third decade and ...
Boffins solve pizza slicing dilemma | SBS News
Dec 11, 2009 ... Here the Pizza theorem says that if you cut the pizza with 3, 7, 11, 15... ... was at Southeast Missouri State University in Cape Girardeau - had ...
Books on the term Pizza theorem
Geometry For Dummies
Mark Ryan, 2008
Learning geometry doesn’t have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with lines, angles, theorems and postulates. It eases you into all the principles and formulas you need to analyze two- and three-dimensional shapes, and it gives you the skills and strategies...
Fete of Combinatorics and Computer Science
Gyula O.H. Katona, Alexander Schrijver, Tamás Szönyi, 2011
For any P, Alice has a two-jump strategy with gain 4|P|/9. More generally, we determine Alice's guaranteed gain for any given number of slices. Theorem 2. For n > 1, let g(n) be the maximum g E [0, 1] such that for any cutting of the pizza into n ...
Nature of Mathematics
Karl J. Smith, 2011
Experience mathematics--and develop problem-solving skills that will benefit you throughout your life--with THE NATURE OF MATHEMATICS. Karl Smith introduces you to proven problem-solving techniques and shows you how to use these techniques to solve unfamiliar problems that you encounter in your day-to-day world. You'll find coverage of interes...
Are: Surface Area, Systolic Geometry, History of ...
Books Llc, 2010
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 29.
How to Guard an Art Gallery and Other Discrete Mathematical Adventures
T.S. Michael, 2009
What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery?Discrete mathematics has the answer to these—and many other—questions ...
S. Shirali, 2002
... M. S., 278 Paths on a grid, 212 Pentomino, 105 Perfect numbers, 221 Pigeon- hole principle, 218 Pizza theorem, 71 Polya, George, 28, 145, 177 Polya enumeration, 216 Polyomino(es), 104, 105 PPT, 231 Primality testing, 1 Prison problem, ...
The American Mathematical Monthly: The Official Journal of ...
2009
We mustn't forget plain old pizza crusts. Confection 3 (Thin Crust of Pizza). Let N > 2 and slice the pizza exactly as in the Cheese Pizza theorem, with the center O not on a cut. Rather than summing areas (cheese) of alternating slices, sum the ...
Proofs Without Words II: More Exercises in Visual Thinking (Classroom Resource Materials) (v. 2)
Roger B. Nelsen, 2001
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing ...

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