Conic Sections

Resources

Conixperiments is a set of hands-on explorations of the basic properties of conic sections covered in this primer. Click the link below to download a copy.

CONIXPERIMENTS [updated July 13, 2017]

You are welcome to download the packet or print out sections for student use, but please do not distribute the packet electronically without permission. Many of the experiments make use of GeoGebra software, available here:

GeoGebra

Included in the packet are copies of Dr. Ortiz's Amazing Conic Graph Paper and Dr. Ortiz's Amazing Central Conic Graph Paper. To access these truly amazing tools as separate PDF documents, please click the links below.

Conic Graph Paper

Central Conic Graph Paper

The primer was prepared largely from historical sources, as cited below. Some students may enjoy reading some of these; the Two New Sciences of Galileo is especially approachable, and includes his exposition on parabolic trajectories. Among the modern works used, students may most benefit from perusing Excursions in Geometry by C. Stanley Ogilvy. Also very useful to the teacher is Practical Conic Sections by J. W. Downs.

Sources

From the Encyclopedia Britannica Great Books of the Western World collection:

  • Euclid, Elements
  • Archimedes, Quadrature of the Parabola
  • Apollonius, Conics
  • Ptolemy, The Almagest
  • Copernicus, On the Revolution of the Heavenly Spheres
  • Kepler, Epitome of Copernican Astronomy
  • Galileo, Concerning the Two New Sciences
  • Newton, Mathematical Principles of Natural Philosophy

H. S. M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, 1989.

J. W. Downs, Practical Conic Sections: The Geometric Properties of Ellipses, Parabolas and Hyperbolas, Dover, Mineola NY, 2003; reprint of 1st ed., Dale Seymour Publications, Palo Alto CA, 1993.

Thomas L. Heath, A History of Greek Mathematics, 2 vols., Dover, Mineola NY, 1981; reprint of 1st ed., Oxford University Press, 1921.

Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press NY, 1972.

Thomas S. Kuhn, The Copernican Revolution, Harvard University Press MA, 1957.

C. Stanley Ogilvy, Excursions in Geometry, Dover, Mineola NY, 1990; corrected reprint of 1st ed., Oxford University Press NY, 1969.

David Eugene Smith, A Source Book in Mathematics, Dover, Mineola NY, 1959; reprint of 1st ed., McGraw-Hill, 1929.

Charles Taylor, An Introduction to the Ancient and Modern Geometry of Conics, Cambridge University Press, 1881.

Albert Waugh, Sundials: Their Theory and Construction, Dover, Mineola NY, 1973.

All mathematical diagrams and animations were created using GeoGebra software.

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Michael Ortiz, Ph.D.
Assistant Professor of Mathematics
Department of Natural and Behavioral Sciences

Sul Ross State University Rio Grande College

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