Project description

Project MATHEMATICS!  videos explore basic topics in high school mathematics  in ways that cannot be done at the chalkboard or in a textbook. They bring mathematics to life with imaginative computer animation, live action, music, special effects, and a sense of humor.                  

Young people are attracted to mathematics through high-quality instructional modules that show mathematics to be understandable, exciting, and eminently worthwhile.  Each module consists of a video together with a workbook/study guide, and explores a basic topic in mathematics that can be integrated into any high school or community college curriculum.  The modules encourage interaction between students and teachers.

Video technology provides a highly efficient way of conveying information.  Visual images make a much greater impact than printed or spoken words, especially when the images are in motion and are accompanied by music and sound effects.  These videos provide a valuable pedagogical tool for supporting mathematics instruction.                        

Millions of viewers have seen one or more of the videos, either in classrooms or on various public television stations. They have been enthusiastically received by teachers and students nationwide and have captured first-place honors at a dozen major film and video festivals.  Translations exist in Hebrew, Portuguese, French, and Spanish.                                        

The videotapes were animated by James F. Blinn, and produced by Professor Tom M. Apostol at the California Institute of Technology in Pasadena, CA.

In the following list of titles, the first nine are available either as separate videotapes (English only), or as 3 bilingual DVDs (English and Spanish), grouped as indicated below.  A workbook/study guide (in English) is available for each title.

List of Titles

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• Similarity Scaling multiplies lengths by the same factor and produces a similar figure. It preserves angles and ratios of lengths of corresponding line segments. Animation shows what happens to perimeters, areas, and volumes under scaling, with various applications from real life
• The Theorem of Pythagoras Several engaging animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles.
• The Story of Pi Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk and transform it to a rectangle with the same area as the disk. Animation shows how Archimedes estimated pi using perimeters of approximating polygons.

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• Sines and Cosines, Part I (Waves) Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion, and as ratios of sides of right triangles. They are related by reflection or translation of their graphs. Animation demonstrates the Gibbs phenomenon of Fourier series.
• Sines and Cosines, Part II  (Trigonometry) This video focuses on trigonometry, with special emphasis on the law of conies and the law of sines, together with applications to The Great Survey of India. The history of surveying instruments is outlined, from Hero’s dioptra to modern orbiting satellites.
• Sines and Cosines, Part III  (Addition formulas) Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy’s Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion.

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• Polynomials Animation shows how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Real-life examples include parabolic trajectories and the use of cubic splines in designing sailboats and computer-generated teapots.
• The Tunnel of Samos This video describes a remarkable engineering work of ancient times: excavating a one-kilometer tunnel straight through the heart of a mountain, using separate crews that dug from the two ends and met in the middle. How did they determine the direction for excavation? The program gives Hero's explanation (ca. 60 A.D.), using similar triangles, as well as alternative methods proposed in modern times.
• Early History of Mathematics This video traces some of the landmark developments in the early history of mathematics, from Babylonian calendars on clay tablets produced 5000 years ago, to the introduction of calculus in the seventeenth century.

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The following two titles are available only as separate videotapes (English only).

• Teachers Workshop This 28-minute tape contains excerpts from a two-day workshop held in 1991 for teachers who have successfully used project materials in their classrooms. In lieu of a workbook, a 90-page transcript is available for this videotape.
• Project MATHEMATICS! Contest In 1991 Project MATHEMATICS! conducted a contest open to all teachers who had used project materials in their classrooms. Entries were judged on the basis of innovative and effective use of the materials. This videotape, and a 30-page booklet produced in lieu of a workbook, shows the classroom implementation of the entries of the first-place winners.

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 E-mail questions about the Project to Tom Apostol