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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. The theorem is so called because it mimics a traditional pizza slicing technique. It shows that if two people share a pizza sliced into 8 pieces (or any multiple of 4 greater than 8), and take alternating slices, then they will each get an equal amount of pizza, irrespective of the central cutting point. Statement Let ''p'' be an interior point of the disk, and let ''n'' be a multiple of 4 that is greater than or equal to 8. Form ''n'' sectors of the disk with equal angles by choosing an arbitrary line through ''p'', rotating the line times by an angle of radians, and slicing the disk on each of the resulting 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'' . History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pizza Theorem Example
Pizza (, ) is a dish of Italian origin consisting of a usually round, flat base of leavened wheat-based dough topped with tomatoes, cheese, and often various other ingredients (such as various types of sausage, anchovies, mushrooms, onions, olives, vegetables, meat, ham, etc.), which is then baked at a high temperature, traditionally in a wood-fired oven. A small pizza is sometimes called a pizzetta. A person who makes pizza is known as a pizzaiolo. In Italy, pizza served in a restaurant is presented unsliced, and is eaten with the use of a knife and fork. In casual settings, however, it is cut into wedges to be eaten while held in the hand. The term ''pizza'' was first recorded in the 10th century in a Latin manuscript from the Southern Italian town of Gaeta in Lazio, on the border with Campania. Modern pizza was invented in Naples, and the dish and its variants have since become popular in many countries. It has become one of the most popular foods in the world and a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Winkler
Peter Mann Winkler is a research mathematician, author of more than 125 research papers in mathematics and patent holder in a broad range of applications, ranging from cryptography to marine navigation.Information listed oPeter Winkler's homepageat Dartmouth. His research areas include discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ..., theory of computation and probability theory. He is currently a professor of mathematics and computer science at Dartmouth College. Peter Winkler studied mathematics at Harvard University and later received his PhD in 1975 from Yale University under the supervision of Angus Macintyre, Angus McIntyre. He has also served as an assistant professor at Stanford, full professor and chair at Emory and as a mathematics research director ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
