The Volumes and Centroids of Some Famous Domes
1988; Taylor & Francis; Volume: 61; Issue: 3 Linguagem: Inglês
10.1080/0025570x.1988.11977364
ISSN1930-0980
Autores Tópico(s)History and Theory of Mathematics
ResumoThe mathematical tourist observes, during his adventures, a great many different surfaces that architects have used over the centuries as models for the vaults they must provide to cover the open spaces of their buildings. If one takes a right circular cylinder of radius r and height h and cuts it into two equal pieces by a plane through the axis, each half is called a barrel, tunnel, or wagon vault, famous examples of which are to be found over the Cloaca Maxima, or great sewer of the ancient Roman Forum (r = 10', h = 800'; see [14, p. 957]), and Carlo Maderno's nave for St. Peter's Basilica, built beginning in 1607 at the command of Pope Paul V (r = 90', h = 320'; see [1, p. 364, and the plan between pages 362 and 363]). Among hemispherical domes, the geometer will most admire that of Hagia Sophia in Constantinople, built during the reign of the Emperor Justinian (527-565); its radius is 53' (cf. [3, p. 548], and [14, p. 958b]). Now everyone knows the volumes of the half-cylinder and hemisphere, and any student of calculus learns how to calculate the centroids of those solids; in this essay, we look into the shapes of some other famous domes, and calculate their volumes and centroids.
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