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Kepler: The Volume of a Wine Barrel - Links and References

Roberto Cardil (MatematicasVisuales)


Link to Kepler biography

Kepler in MacTutor History of Mathematics Archive

A biography of Johannes Kepler (1571-1630)

Link to Kepler's Nova stereometria

Original Latin version of Kepler's Nova stereometria (Posner Memorial Collection, Carnegie Mellon University Libraries)

Kepler's German version of his Nova stereometria (two pages, Loci: Convergence Mathematical Treasures)

Link to circle animation

Kepler in MatematicasVisuales - The Area of a Circle

Kepler's intuitive infinitesimal approach to determine the area of a circle

Link to sphere animation

Kepler in MatematicasVisuales - The Volume of a Sphere

Kepler's intuitive infinitesimal approach to determine the volume of a sphere
Link to MathWorld: Kepler's Lemon

Kepler in MathWorld: Lemon

Kepler in MathWorld: Apple

Two solids of revolution defined by Kepler

Link to article on Archimedes' Method

Archimedes' Method for Computing Areas and Volumes

Article by Gabriela Sanchis in Loci: Convergence explaining Archimedes' Method based on the Law of the Lever

Link to animation illustrating Archimedes' method

Archimedes in MatematicasVisuales - Area of a Parabolic Segment

Archimedes used infinitesimal methods to discover areas and volumes 1800 years before Kepler and Cavalieri.

Link to Convergence article on isoperimetric problem

The Sagacity of Circles: A History of the Isoperimetric Problem

Article by Jennifer Wiegert in Loci: Convergence summarizing the history of the problem of finding the region of greatest area bounded by a given perimeter


Link to Loci article on box optimization

Thinking Outside the Box - or Maybe Just About the Box

Article by David Meel and Thomas Hern in Loci presenting a box optimization problem more realistic and hence more complex than the standard one.
































Margaret E. Baron, The Origins of the Infinitesimal Calculus, Dover Publications, New York, 1987; originally published in 1969 by Pergamon Press, Oxford, England.

Carl B. Boyer, The History of the Calculus and its Conceptual Development, Dover Publications, New York, 1959, reprint of 1949 edition of Boyer's The Concepts of the Calculus: A Critical and Historical Discussion of the Derivative and the Integral, Hafner Publishing, originally published in 1939.

Roberto Cardil, Kepler: The Best Proportions for a Wine Barrel (interactive applet), MatematicasVisuales, posted 2009-2010.

Roberto Cardil, Kepler: The Volume of a Wine Barrel (interactive applet), MatematicasVisuales, posted 8 January 2010.

Roberto Cardil, "Kepler: The Volume of a Wine Barrel" (copy of this article with four interactive applets), MatematicasVisuales, posted 2011

Roberto Cardil, MatematicasVisuales:

C.H. Edwards, The Historical Development of the Calculus, Springer-Verlag, New York, 1979.

Kepler, Johannes, Nova stereometria doliorum vinariorum, Linz, 1615, held in the Posner Memorial Collection of the Carnegie Mellon University Libraries, Pittsburgh, Pennsylvania, call number 520 K38PN, available in electronic format:

Felix Klein, Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis (especially pp. 207-210), Dover Publications, New York, 2004; originally published in 1908 in Leipzig.

Dirk J. Struik (ed.), A Source Book in Mathematics, 1200-1800 (see pp. 192-197: "Kepler. Integration Methods"), Harvard University Press, Cambridge, MA, 1969.

Otto Toeplitz, The Calculus: A Genetic Approach (especially pp. 80-83), University Of Chicago Press, 1963.

Roberto Cardil (MatematicasVisuales), "Kepler: The Volume of a Wine Barrel - Links and References," Convergence (January 2012), DOI:10.4169/loci003499