Pizza theorem

Pizza Theorem is a geometric principle in mathematics, specifically in the field of geometry. It is named after the popular Italian dish, pizza, due to the visual similarity between the theorem's demonstration and the process of slicing a pizza.

Overview

The Pizza Theorem states that if a pizza is sliced from the center by a certain number of straight lines (assuming an even number), the sum of the areas of alternate slices is always equal. This theorem is applicable in various mathematical and practical contexts, including area calculation and probability theory.

Mathematical Explanation

Consider a pizza as a circular disk. If it is sliced into an even number of equal and alternating sectors, starting from the center of the disk, the sum of the areas of alternating sectors will be equal. This is true regardless of the angle at which the first cut is made.

History

The Pizza Theorem was first proposed by L.J. Upton, a mathematician, in 1967. It has since been the subject of numerous mathematical papers and has found applications in various fields of study.

Applications

The Pizza Theorem has found applications in various fields of study. In probability theory, it is used to solve problems related to random points on a disk. In computer science, it is used in algorithms related to disk scheduling in operating systems.

Proof

The proof of the Pizza Theorem involves the use of integral calculus and trigonometry. It is based on the principle of symmetry in geometry and the properties of circular sectors.

See Also

• Circle
• Geometry
• Mathematics
• Probability Theory
• Computer Science

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Pizza_theorem

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  Example of the Pizza Theorem
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  Visual proof of the Pizza Theorem
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  Illustration of the Pizza Theorem