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Cavalieri’s Principle By Faraz Taheri
Abstract Cavalieri’s Principle, named after Bonaventura Cavalieri, is a geometrical method to find the area or volume of an object on a plane or in a three-space respectively.
1 Introduction Cavalieri’s Principle, aka method of indivisibles, presumes lines are made of an infinite number of points, planes are made of an infinite number of lines and volumes are made up of an infinite number of planes. And therefore it aims to find the sum of infinite lengths or areas. It basically uses the concept of integration without using the integral notation. 1.1 Two-dimensional space Suppose the baselines of two regions on a plane are placed on a single line. If every line drawn parallel to the baselines, makes 2 line segments of equal length, the areas of those regions are equal.
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