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Volumes

In: Calculator Calculus

Author

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  • George McCarty

    (University of California)

Abstract

In his Mathematical Thought from Ancient to Modern Times (see Bibliography) Morris Kline describes the four major types of problems that led to the creation of the calculus. These are the problems of calculating: (i) Motion: The distance traveled by an object, its velocity, its acceleration, and the relationships between these quantities. (ii) Tangents: The tangents to curves and to solids. These were needed in geometry, and they were also useful in optics and in the study of motion. (iii) Extremes: Maxima and minima for various functions. Notably, Galileo (1564–1642) found the correct angle (π/4) to fire a cannon for maximal range. (iv) Lengths, areas, and volumes: The distance traveled by a planet around the sun, areas bounded by curves, volumes bounded by curved surfaces, centers of gravity, and total gravitational attraction of a body.

Suggested Citation

  • George McCarty, 1982. "Volumes," Springer Books, in: Calculator Calculus, chapter 9, pages 117-129, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-6484-9_9
    DOI: 10.1007/978-1-4684-6484-9_9
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