Cavalieri's Principle

Simply stated, "Cavalieri's principle says that solids with equal altitudes and identical cross-sectional areas at each height have the same volume [which] follows immediately from the definition of volume, because the cross-sectional area function A(x) and the interval [a,b] are the same for both solids"(Hass, Weir, & Thomas, 2006, p. 393).

We can frankly state Cavaleri's Principle as a method in which two solids are cut into slices and if each slice in one solid has equal area to each slice in the other solid then both solids have equal volume.

Cavalieri's Principle, also known as the Method of Indivisibles, is important because it has helped in the discovery of formulas for the volumes of solids. The Method of Indivisbles is also important because it is a simple method which has helped in many different scientific studies.

One example of a scientific study where Cavalieri's Principle came into play was in volume estimation for Laser Confocal Microscopy, which is, "a technique for obtaining high-resolution optical images with depth selectivity" (“Confocal laser scanning microscopy,” 2012). Instead of comparison between each confocal section used in the study, Cavalieri's principle was applied in order to lessen the amount in the overall data set. (Prakash, Smithson, & Sieck, 1994)

Another study was performed in regards to the volume and surface area of lungs. In the study, Cavalieri's principle was used, along with fluid displacement, in order to gain the necessary information for the study. (Michel & Cruz-Orive, 1988)

Cavalieri's Principle has helped in many other studies, such as studies in comparisons of trauma site adhesions (Gorvy, Herrick, Shah, & Ferguson, 2005) and studies of comparative tympanic cavity volumes (Kürkçüoglu A et al., n.d.). Overall, the Method of Indivisibles is an efficient way for mathematicians and researchers to find and compare volumes of solids.